LMFDB - Embedded newform 38.6.c.a.7.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,6,Mod(7,38)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("38.7");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	38.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.09458515289$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 133x^{4} - 60x^{3} + 17689x^{2} - 3990x + 900 $ x^6 + 133x^4 - 60x^3 + 17689x^2 - 3990x + 900
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.3
Root			$-5.82187 + 10.0838i$ of defining polynomial
Character	$\chi$	$=$	38.7
Dual form			38.6.c.a.11.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 3.46410i) q^{2} +(9.14373 + 15.8374i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(14.1445 + 24.4990i) q^{5} +(-36.5749 + 63.3496i) q^{6} -10.8501 q^{7} -64.0000 q^{8} +(-45.7157 + 79.1819i) q^{9} +O(q^{10})$	\(q+(2.00000 + 3.46410i) q^{2} +(9.14373 + 15.8374i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(14.1445 + 24.4990i) q^{5} +(-36.5749 + 63.3496i) q^{6} -10.8501 q^{7} -64.0000 q^{8} +(-45.7157 + 79.1819i) q^{9} +(-56.5781 + 97.9961i) q^{10} -86.1360 q^{11} -292.599 q^{12} +(-65.2853 + 113.077i) q^{13} +(-21.7003 - 37.5860i) q^{14} +(-258.667 + 448.025i) q^{15} +(-128.000 - 221.703i) q^{16} +(240.027 + 415.738i) q^{17} -365.725 q^{18} +(1171.25 + 1050.85i) q^{19} -452.624 q^{20} +(-99.2108 - 171.838i) q^{21} +(-172.272 - 298.384i) q^{22} +(622.601 - 1078.38i) q^{23} +(-585.199 - 1013.59i) q^{24} +(1162.37 - 2013.28i) q^{25} -522.282 q^{26} +2771.81 q^{27} +(86.8012 - 150.344i) q^{28} +(1638.13 - 2837.32i) q^{29} -2069.34 q^{30} +5823.21 q^{31} +(512.000 - 886.810i) q^{32} +(-787.605 - 1364.17i) q^{33} +(-960.107 + 1662.95i) q^{34} +(-153.470 - 265.818i) q^{35} +(-731.451 - 1266.91i) q^{36} -1285.00 q^{37} +(-1297.75 + 6159.01i) q^{38} -2387.80 q^{39} +(-905.249 - 1567.94i) q^{40} +(-1927.28 - 3338.14i) q^{41} +(396.843 - 687.353i) q^{42} +(453.563 + 785.594i) q^{43} +(689.088 - 1193.54i) q^{44} -2586.50 q^{45} +4980.81 q^{46} +(-5362.72 + 9288.50i) q^{47} +(2340.80 - 4054.38i) q^{48} -16689.3 q^{49} +9298.92 q^{50} +(-4389.48 + 7602.80i) q^{51} +(-1044.56 - 1809.24i) q^{52} +(-14584.0 + 25260.2i) q^{53} +(5543.61 + 9601.82i) q^{54} +(-1218.35 - 2110.25i) q^{55} +694.409 q^{56} +(-5933.16 + 28158.2i) q^{57} +13105.0 q^{58} +(-4754.96 - 8235.84i) q^{59} +(-4138.68 - 7168.40i) q^{60} +(690.342 - 1195.71i) q^{61} +(11646.4 + 20172.2i) q^{62} +(496.022 - 859.135i) q^{63} +4096.00 q^{64} -3693.71 q^{65} +(3150.42 - 5456.69i) q^{66} +(34749.5 - 60188.0i) q^{67} -7680.85 q^{68} +22771.6 q^{69} +(613.880 - 1063.27i) q^{70} +(-29670.7 - 51391.2i) q^{71} +(2925.80 - 5067.64i) q^{72} +(-17937.1 - 31067.9i) q^{73} +(-2570.00 - 4451.37i) q^{74} +42513.4 q^{75} +(-23930.9 + 7822.47i) q^{76} +934.589 q^{77} +(-4775.61 - 8271.59i) q^{78} +(-49097.6 - 85039.5i) q^{79} +(3621.00 - 6271.75i) q^{80} +(36453.6 + 63139.4i) q^{81} +(7709.10 - 13352.6i) q^{82} +45809.3 q^{83} +3174.75 q^{84} +(-6790.12 + 11760.8i) q^{85} +(-1814.25 + 3142.37i) q^{86} +59914.4 q^{87} +5512.71 q^{88} +(-46733.8 + 80945.3i) q^{89} +(-5173.01 - 8959.91i) q^{90} +(708.354 - 1226.91i) q^{91} +(9961.61 + 17254.0i) q^{92} +(53245.8 + 92224.5i) q^{93} -42901.8 q^{94} +(-9178.05 + 43558.1i) q^{95} +18726.4 q^{96} +(13653.9 + 23649.3i) q^{97} +(-33378.5 - 57813.3i) q^{98} +(3937.77 - 6820.41i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 12 q^{2} - 15 q^{3} - 48 q^{4} + 14 q^{5} + 60 q^{6} - 624 q^{7} - 384 q^{8} - 410 q^{9}+O(q^{10}) $ 6 * q + 12 * q^2 - 15 * q^3 - 48 * q^4 + 14 * q^5 + 60 * q^6 - 624 * q^7 - 384 * q^8 - 410 * q^9	\( 6 q + 12 q^{2} - 15 q^{3} - 48 q^{4} + 14 q^{5} + 60 q^{6} - 624 q^{7} - 384 q^{8} - 410 q^{9} - 56 q^{10} - 938 q^{11} + 480 q^{12} - 736 q^{13} - 1248 q^{14} + 954 q^{15} - 768 q^{16} - 1000 q^{17} - 3280 q^{18} + 5681 q^{19} - 448 q^{20} + 5816 q^{21} - 1876 q^{22} - 2168 q^{23} + 960 q^{24} - 3187 q^{25} - 5888 q^{26} + 16650 q^{27} + 4992 q^{28} + 1486 q^{29} + 7632 q^{30} + 396 q^{31} + 3072 q^{32} + 3589 q^{33} + 4000 q^{34} - 4992 q^{35} - 6560 q^{36} + 20060 q^{37} + 13528 q^{38} + 37480 q^{39} - 896 q^{40} - 19551 q^{41} - 23264 q^{42} - 5058 q^{43} + 7504 q^{44} - 114408 q^{45} - 17344 q^{46} + 7426 q^{47} - 3840 q^{48} - 1898 q^{49} - 25496 q^{50} - 51980 q^{51} - 11776 q^{52} - 3156 q^{53} + 33300 q^{54} + 8540 q^{55} + 39936 q^{56} - 60762 q^{57} + 11888 q^{58} - 325 q^{59} + 15264 q^{60} + 19674 q^{61} + 792 q^{62} + 82320 q^{63} + 24576 q^{64} - 149516 q^{65} - 14356 q^{66} + 61837 q^{67} + 32000 q^{68} + 64072 q^{69} + 19968 q^{70} + 5760 q^{71} + 26240 q^{72} + 18747 q^{73} + 40120 q^{74} + 219654 q^{75} - 36784 q^{76} + 107504 q^{77} + 74960 q^{78} + 80158 q^{79} + 3584 q^{80} - 59939 q^{81} + 78204 q^{82} - 335402 q^{83} - 186112 q^{84} + 102510 q^{85} + 20232 q^{86} + 125388 q^{87} + 60032 q^{88} - 166228 q^{89} - 228816 q^{90} + 136784 q^{91} - 34688 q^{92} + 368074 q^{93} + 59408 q^{94} - 171266 q^{95} - 30720 q^{96} - 86615 q^{97} - 3796 q^{98} + 28646 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 - 15 * q^3 - 48 * q^4 + 14 * q^5 + 60 * q^6 - 624 * q^7 - 384 * q^8 - 410 * q^9 - 56 * q^10 - 938 * q^11 + 480 * q^12 - 736 * q^13 - 1248 * q^14 + 954 * q^15 - 768 * q^16 - 1000 * q^17 - 3280 * q^18 + 5681 * q^19 - 448 * q^20 + 5816 * q^21 - 1876 * q^22 - 2168 * q^23 + 960 * q^24 - 3187 * q^25 - 5888 * q^26 + 16650 * q^27 + 4992 * q^28 + 1486 * q^29 + 7632 * q^30 + 396 * q^31 + 3072 * q^32 + 3589 * q^33 + 4000 * q^34 - 4992 * q^35 - 6560 * q^36 + 20060 * q^37 + 13528 * q^38 + 37480 * q^39 - 896 * q^40 - 19551 * q^41 - 23264 * q^42 - 5058 * q^43 + 7504 * q^44 - 114408 * q^45 - 17344 * q^46 + 7426 * q^47 - 3840 * q^48 - 1898 * q^49 - 25496 * q^50 - 51980 * q^51 - 11776 * q^52 - 3156 * q^53 + 33300 * q^54 + 8540 * q^55 + 39936 * q^56 - 60762 * q^57 + 11888 * q^58 - 325 * q^59 + 15264 * q^60 + 19674 * q^61 + 792 * q^62 + 82320 * q^63 + 24576 * q^64 - 149516 * q^65 - 14356 * q^66 + 61837 * q^67 + 32000 * q^68 + 64072 * q^69 + 19968 * q^70 + 5760 * q^71 + 26240 * q^72 + 18747 * q^73 + 40120 * q^74 + 219654 * q^75 - 36784 * q^76 + 107504 * q^77 + 74960 * q^78 + 80158 * q^79 + 3584 * q^80 - 59939 * q^81 + 78204 * q^82 - 335402 * q^83 - 186112 * q^84 + 102510 * q^85 + 20232 * q^86 + 125388 * q^87 + 60032 * q^88 - 166228 * q^89 - 228816 * q^90 + 136784 * q^91 - 34688 * q^92 + 368074 * q^93 + 59408 * q^94 - 171266 * q^95 - 30720 * q^96 - 86615 * q^97 - 3796 * q^98 + 28646 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.00000	+	3.46410i	0.353553	+	0.612372i
$2$	2.00000	+	3.46410i	0.353553	+	0.612372i
$3$	9.14373	+	15.8374i	0.586571	+	1.01597i	0.994678	+	0.103036i	$0.0328557\pi$
$3$	9.14373	+	15.8374i	0.586571	+	1.01597i	−0.408107	+	0.912934i	$0.633811\pi$
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	14.1445	+	24.4990i	0.253025	+	0.438252i	0.964357	−	0.264604i	$-0.0852412\pi$
$5$	14.1445	+	24.4990i	0.253025	+	0.438252i	−0.711332	+	0.702856i	$0.751908\pi$
$6$	−36.5749	+	63.3496i	−0.414768	+	0.718399i
$7$	−10.8501			−0.0836932			−0.0418466	−	0.999124i	$-0.513324\pi$
$7$	−10.8501			−0.0836932			−0.0418466	+	0.999124i	$0.513324\pi$
$8$	−64.0000			−0.353553
$9$	−45.7157	+	79.1819i	−0.188130	+	0.325851i
$10$	−56.5781	+	97.9961i	−0.178916	+	0.309891i
$11$	−86.1360			−0.214636			−0.107318	−	0.994225i	$-0.534226\pi$
$11$	−86.1360			−0.214636			−0.107318	+	0.994225i	$0.534226\pi$
$12$	−292.599			−0.586571
$13$	−65.2853	+	113.077i	−0.107141	+	0.185574i	−0.914611	−	0.404335i	$-0.867503\pi$
$13$	−65.2853	+	113.077i	−0.107141	+	0.185574i	0.807470	+	0.589909i	$0.200836\pi$
$14$	−21.7003	−	37.5860i	−0.0295900	−	0.0512514i
$15$	−258.667	+	448.025i	−0.296834	+	0.514131i
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	240.027	+	415.738i	0.201436	+	0.348898i	0.948991	−	0.315302i	$-0.102106\pi$
$17$	240.027	+	415.738i	0.201436	+	0.348898i	−0.747555	+	0.664200i	$0.768773\pi$
$18$	−365.725			−0.266056
$19$	1171.25	+	1050.85i	0.744327	+	0.667815i
$19$	1171.25	+	1050.85i	0.744327	+	0.667815i
$20$	−452.624			−0.253025
$21$	−99.2108	−	171.838i	−0.0490920	−	0.0850298i
$22$	−172.272	−	298.384i	−0.0758854	−	0.131437i
$23$	622.601	−	1078.38i	0.245409	−	0.425061i	−0.716838	−	0.697240i	$-0.754411\pi$
$23$	622.601	−	1078.38i	0.245409	−	0.425061i	0.962246	+	0.272180i	$0.0877445\pi$
$24$	−585.199	−	1013.59i	−0.207384	−	0.359200i
$25$	1162.37	−	2013.28i	0.371957	−	0.644248i
$26$	−522.282			−0.151521
$27$	2771.81			0.731734
$28$	86.8012	−	150.344i	0.0209233	−	0.0362402i
$29$	1638.13	−	2837.32i	0.361703	−	0.626489i	−0.626538	−	0.779391i	$-0.715529\pi$
$29$	1638.13	−	2837.32i	0.361703	−	0.626489i	0.988241	+	0.152902i	$0.0488620\pi$
$30$	−2069.34			−0.419786
$31$	5823.21			1.08832			0.544162	−	0.838980i	$-0.316848\pi$
$31$	5823.21			1.08832			0.544162	+	0.838980i	$0.316848\pi$
$32$	512.000	−	886.810i	0.0883883	−	0.153093i
$33$	−787.605	−	1364.17i	−0.125899	−	0.218064i
$34$	−960.107	+	1662.95i	−0.142437	+	0.246708i
$35$	−153.470	−	265.818i	−0.0211765	−	0.0366787i
$36$	−731.451	−	1266.91i	−0.0940652	−	0.162926i
$37$	−1285.00			−0.154312			−0.0771558	−	0.997019i	$-0.524584\pi$
$37$	−1285.00			−0.154312			−0.0771558	+	0.997019i	$0.524584\pi$
$38$	−1297.75	+	6159.01i	−0.145792	+	0.691914i
$39$	−2387.80			−0.251384
$40$	−905.249	−	1567.94i	−0.0894578	−	0.154945i
$41$	−1927.28	−	3338.14i	−0.179054	−	0.310131i	0.762503	−	0.646985i	$-0.223970\pi$
$41$	−1927.28	−	3338.14i	−0.179054	−	0.310131i	−0.941557	+	0.336854i	$0.890637\pi$
$42$	396.843	−	687.353i	0.0347133	−	0.0601252i
$43$	453.563	+	785.594i	0.0374082	+	0.0647928i	0.884123	−	0.467254i	$-0.154757\pi$
$43$	453.563	+	785.594i	0.0374082	+	0.0647928i	−0.846715	+	0.532046i	$0.821423\pi$
$44$	689.088	−	1193.54i	0.0536591	−	0.0929403i
$45$	−2586.50			−0.190407
$46$	4980.81			0.347060
$47$	−5362.72	+	9288.50i	−0.354112	+	0.613340i	−0.986966	−	0.160932i	$-0.948550\pi$
$47$	−5362.72	+	9288.50i	−0.354112	+	0.613340i	0.632854	+	0.774271i	$0.281883\pi$
$48$	2340.80	−	4054.38i	0.146643	−	0.253993i
$49$	−16689.3			−0.992995
$50$	9298.92			0.526027
$51$	−4389.48	+	7602.80i	−0.236313	+	0.409306i
$52$	−1044.56	−	1809.24i	−0.0535706	−	0.0927870i
$53$	−14584.0	+	25260.2i	−0.713158	+	1.23523i	0.250507	+	0.968115i	$0.419403\pi$
$53$	−14584.0	+	25260.2i	−0.713158	+	1.23523i	−0.963666	+	0.267112i	$0.913931\pi$
$54$	5543.61	+	9601.82i	0.258707	+	0.448094i
$55$	−1218.35	−	2110.25i	−0.0543083	−	0.0940647i
$56$	694.409			0.0295900
$57$	−5933.16	+	28158.2i	−0.241879	+	1.14794i
$58$	13105.0			0.511526
$59$	−4754.96	−	8235.84i	−0.177835	−	0.308019i	0.763304	−	0.646040i	$-0.223576\pi$
$59$	−4754.96	−	8235.84i	−0.177835	−	0.308019i	−0.941139	+	0.338021i	$0.890243\pi$
$60$	−4138.68	−	7168.40i	−0.148417	−	0.257066i
$61$	690.342	−	1195.71i	0.0237542	−	0.0411434i	−0.853904	−	0.520431i	$-0.825771\pi$
$61$	690.342	−	1195.71i	0.0237542	−	0.0411434i	0.877658	+	0.479287i	$0.159105\pi$
$62$	11646.4	+	20172.2i	0.384780	+	0.666459i
$63$	496.022	−	859.135i	0.0157452	−	0.0272716i
$64$	4096.00			0.125000
$65$	−3693.71			−0.108438
$66$	3150.42	−	5456.69i	0.0890243	−	0.154195i
$67$	34749.5	−	60188.0i	0.945719	−	1.63803i	0.191413	−	0.981510i	$-0.438693\pi$
$67$	34749.5	−	60188.0i	0.945719	−	1.63803i	0.754306	−	0.656523i	$-0.227974\pi$
$68$	−7680.85			−0.201436
$69$	22771.6			0.575798
$70$	613.880	−	1063.27i	0.0149740	−	0.0259358i
$71$	−29670.7	−	51391.2i	−0.698526	−	1.20988i	−0.968978	−	0.247148i	$-0.920506\pi$
$71$	−29670.7	−	51391.2i	−0.698526	−	1.20988i	0.270452	−	0.962733i	$-0.412827\pi$
$72$	2925.80	−	5067.64i	0.0665141	−	0.115206i
$73$	−17937.1	−	31067.9i	−0.393953	−	0.682346i	0.599014	−	0.800738i	$-0.295559\pi$
$73$	−17937.1	−	31067.9i	−0.393953	−	0.682346i	−0.992967	+	0.118392i	$0.962226\pi$
$74$	−2570.00	−	4451.37i	−0.0545574	−	0.0944962i
$75$	42513.4			0.872716
$76$	−23930.9	+	7822.47i	−0.475254	+	0.155350i
$77$	934.589			0.0179636
$78$	−4775.61	−	8271.59i	−0.0888775	−	0.153940i
$79$	−49097.6	−	85039.5i	−0.885100	−	1.53304i	−0.845599	−	0.533819i	$-0.820756\pi$
$79$	−49097.6	−	85039.5i	−0.885100	−	1.53304i	−0.0395013	−	0.999220i	$-0.512577\pi$
$80$	3621.00	−	6271.75i	0.0632562	−	0.109563i
$81$	36453.6	+	63139.4i	0.617344	+	1.06927i
$82$	7709.10	−	13352.6i	0.126610	−	0.219295i
$83$	45809.3			0.729892			0.364946	−	0.931029i	$-0.381087\pi$
$83$	45809.3			0.729892			0.364946	+	0.931029i	$0.381087\pi$
$84$	3174.75			0.0490920
$85$	−6790.12	+	11760.8i	−0.101937	+	0.176559i
$86$	−1814.25	+	3142.37i	−0.0264516	+	0.0458154i
$87$	59914.4			0.848658
$88$	5512.71			0.0758854
$89$	−46733.8	+	80945.3i	−0.625397	+	1.08322i	0.363067	+	0.931763i	$0.381730\pi$
$89$	−46733.8	+	80945.3i	−0.625397	+	1.08322i	−0.988464	+	0.151457i	$0.951604\pi$
$90$	−5173.01	−	8959.91i	−0.0673189	−	0.116600i
$91$	708.354	−	1226.91i	0.00896700	−	0.0155313i
$92$	9961.61	+	17254.0i	0.122704	+	0.212530i
$93$	53245.8	+	92224.5i	0.638379	+	1.10570i
$94$	−42901.8			−0.500790
$95$	−9178.05	+	43558.1i	−0.104338	+	0.495177i
$96$	18726.4			0.207384
$97$	13653.9	+	23649.3i	0.147342	+	0.255205i	0.930244	−	0.366940i	$-0.119595\pi$
$97$	13653.9	+	23649.3i	0.147342	+	0.255205i	−0.782902	+	0.622145i	$0.786261\pi$
$98$	−33378.5	−	57813.3i	−0.351077	−	0.608083i
$99$	3937.77	−	6820.41i	0.0403796	−	0.0699395i
$100$	18597.8	+	32212.4i	0.185978	+	0.322124i
$101$	−52530.7	+	90985.8i	−0.512401	+	0.887504i	0.487496	+	0.873125i	$0.337910\pi$
$101$	−52530.7	+	90985.8i	−0.512401	+	0.887504i	−0.999897	+	0.0143786i	$0.995423\pi$
$102$	−35115.8			−0.334197
$103$	−41650.6			−0.386837			−0.193418	−	0.981116i	$-0.561957\pi$
$103$	−41650.6			−0.386837			−0.193418	+	0.981116i	$0.561957\pi$
$104$	4178.26	−	7236.95i	0.0378802	−	0.0656104i
$105$	2806.58	−	4861.14i	0.0248430	−	0.0430293i
$106$	−116672.			−1.00856
$107$	105758.			0.893006			0.446503	−	0.894782i	$-0.352669\pi$
$107$	105758.			0.893006			0.446503	+	0.894782i	$0.352669\pi$
$108$	−22174.5	+	38407.3i	−0.182934	+	0.316850i
$109$	−106322.	−	184156.i	−0.857153	−	1.48463i	−0.874633	−	0.484785i	$-0.838898\pi$
$109$	−106322.	−	184156.i	−0.857153	−	1.48463i	0.0174807	−	0.999847i	$-0.494435\pi$
$110$	4873.41	−	8440.99i	0.0384018	−	0.0665138i
$111$	−11749.7	−	20351.1i	−0.0905147	−	0.156776i
$112$	1388.82	+	2405.50i	0.0104617	+	0.0181201i
$113$	−5935.11			−0.0437253			−0.0218626	−	0.999761i	$-0.506960\pi$
$113$	−5935.11			−0.0437253			−0.0218626	+	0.999761i	$0.506960\pi$
$114$	−109409.	+	35763.3i	−0.788481	+	0.257736i
$115$	35225.5			0.248378
$116$	26210.0	+	45397.1i	0.180852	+	0.313244i
$117$	−5969.12	−	10338.8i	−0.0403130	−	0.0698242i
$118$	19019.9	−	32943.4i	0.125748	−	0.217802i
$119$	−2604.32	−	4510.82i	−0.0168588	−	0.0292004i
$120$	16554.7	−	28673.6i	0.104947	−	0.181773i
$121$	−153632.			−0.953931
$122$	5522.73			0.0335935
$123$	35245.0	−	61046.1i	0.210056	−	0.363827i
$124$	−46585.7	+	80688.7i	−0.272081	+	0.471258i
$125$	154168.			0.882507
$126$	3968.17			0.0222671
$127$	36868.9	−	63858.7i	0.202839	−	0.351327i	−0.746603	−	0.665269i	$-0.768317\pi$
$127$	36868.9	−	63858.7i	0.202839	−	0.351327i	0.949442	+	0.313943i	$0.101650\pi$
$128$	8192.00	+	14189.0i	0.0441942	+	0.0765466i
$129$	−8294.51	+	14366.5i	−0.0438850	+	0.0760111i
$130$	−7387.43	−	12795.4i	−0.0383385	−	0.0664042i
$131$	160371.	+	277770.i	0.816483	+	1.41419i	0.908258	+	0.418410i	$0.137413\pi$
$131$	160371.	+	277770.i	0.816483	+	1.41419i	−0.0917751	+	0.995780i	$0.529254\pi$
$132$	25203.4			0.125899
$133$	−12708.2	−	11401.9i	−0.0622952	−	0.0558916i
$134$	277996.			1.33745
$135$	39205.9	+	67906.5i	0.185147	+	0.320684i
$136$	−15361.7	−	26607.3i	−0.0712184	−	0.123354i
$137$	5302.18	−	9183.64i	0.0241353	−	0.0418036i	−0.853705	−	0.520756i	$-0.825650\pi$
$137$	5302.18	−	9183.64i	0.0241353	−	0.0418036i	0.877841	+	0.478953i	$0.158983\pi$
$138$	45543.2	+	78883.1i	0.203575	+	0.352603i
$139$	83183.6	−	144078.i	0.365175	−	0.632501i	−0.623629	−	0.781720i	$-0.714343\pi$
$139$	83183.6	−	144078.i	0.365175	−	0.632501i	0.988804	+	0.149219i	$0.0476759\pi$
$140$	4911.04			0.0211765
$141$	−196141.			−0.830847
$142$	118683.	−	205565.i	0.493932	−	0.855516i
$143$	5623.41	−	9740.04i	0.0229964	−	0.0398309i
$144$	23406.4			0.0940652
$145$	92682.0			0.366080
$146$	71748.2	−	124272.i	0.278567	−	0.482491i
$147$	−152602.	−	264315.i	−0.582462	−	1.00885i
$148$	10280.0	−	17805.5i	0.0385779	−	0.0668189i
$149$	−99141.6	−	171718.i	−0.365839	−	0.633652i	0.623071	−	0.782165i	$-0.285885\pi$
$149$	−99141.6	−	171718.i	−0.365839	−	0.633652i	−0.988910	+	0.148513i	$0.952551\pi$
$150$	85026.9	+	147271.i	0.308552	+	0.534427i
$151$	−151096.			−0.539274			−0.269637	−	0.962962i	$-0.586904\pi$
$151$	−151096.			−0.539274			−0.269637	+	0.962962i	$0.586904\pi$
$152$	−74959.7	−	67254.3i	−0.263159	−	0.236108i
$153$	−43891.9			−0.151585
$154$	1869.18	+	3237.51i	0.00635110	+	0.0110004i
$155$	82366.4	+	142663.i	0.275373	+	0.476960i
$156$	19102.4	−	33086.4i	0.0628459	−	0.108852i
$157$	−204676.	−	354509.i	−0.662701	−	1.14783i	−0.979903	−	0.199474i	$-0.936077\pi$
$157$	−204676.	−	354509.i	−0.662701	−	1.14783i	0.317202	−	0.948358i	$-0.397257\pi$
$158$	196390.	−	340158.i	0.625860	−	1.08402i
$159$	−533408.			−1.67327
$160$	28968.0			0.0894578
$161$	−6755.31	+	11700.5i	−0.0205391	+	0.0355747i
$162$	−145814.	+	252558.i	−0.436528	+	0.756089i
$163$	455479.			1.34276			0.671382	−	0.741112i	$-0.265701\pi$
$163$	455479.			1.34276			0.671382	+	0.741112i	$0.265701\pi$
$164$	61672.8			0.179054
$165$	22280.6	−	38591.1i	0.0637113	−	0.110351i
$166$	91618.7	+	158688.i	0.258056	+	0.446966i
$167$	−116591.	+	201942.i	−0.323500	+	0.560319i	−0.981208	−	0.192954i	$-0.938193\pi$
$167$	−116591.	+	201942.i	−0.323500	+	0.560319i	0.657707	+	0.753274i	$0.271526\pi$
$168$	6349.49	+	10997.6i	0.0173566	+	0.0300626i
$169$	177122.	+	306785.i	0.477042	+	0.826260i
$170$	−54321.0			−0.144160
$171$	−136752.	+	44701.2i	−0.357639	+	0.116904i
$172$	−14514.0			−0.0374082
$173$	297636.	+	515521.i	0.756085	+	1.30958i	0.944833	+	0.327552i	$0.106224\pi$
$173$	297636.	+	515521.i	0.756085	+	1.30958i	−0.188748	+	0.982026i	$0.560443\pi$
$174$	119829.	+	207549.i	0.300046	+	0.519695i
$175$	−12611.8	+	21844.3i	−0.0311303	+	0.0539192i
$176$	11025.4	+	19096.6i	0.0268295	+	0.0464701i
$177$	86956.2	−	150613.i	0.208626	−	0.361350i
$178$	−373870.			−0.884445
$179$	−452122.			−1.05469			−0.527343	−	0.849653i	$-0.676812\pi$
$179$	−452122.			−1.05469			−0.527343	+	0.849653i	$0.676812\pi$
$180$	20692.0	−	35839.6i	0.0476016	−	0.0824484i
$181$	−46764.2	+	80997.9i	−0.106100	+	0.183771i	−0.914187	−	0.405292i	$-0.867170\pi$
$181$	−46764.2	+	80997.9i	−0.106100	+	0.183771i	0.808087	+	0.589063i	$0.200503\pi$
$182$	5666.84			0.0126813
$183$	25249.2			0.0557340
$184$	−39846.5	+	69016.1i	−0.0867651	+	0.150282i
$185$	−18175.7	−	31481.2i	−0.0390447	−	0.0676273i
$186$	−212983.	+	368898.i	−0.451402	+	0.781851i
$187$	−20675.0	−	35810.1i	−0.0432355	−	0.0748861i
$188$	−85803.5	−	148616.i	−0.177056	−	0.306670i
$189$	−30074.5			−0.0612412
$190$	−169246.	+	55322.5i	−0.340121	+	0.111178i
$191$	−136011.			−0.269768			−0.134884	−	0.990861i	$-0.543066\pi$
$191$	−136011.			−0.269768			−0.134884	+	0.990861i	$0.543066\pi$
$192$	37452.7	+	64870.0i	0.0733213	+	0.126996i
$193$	183790.	+	318334.i	0.355164	+	0.615163i	0.987146	−	0.159820i	$-0.0510915\pi$
$193$	183790.	+	318334.i	0.355164	+	0.615163i	−0.631982	+	0.774983i	$0.717758\pi$
$194$	−54615.7	+	94597.1i	−0.104187	+	0.180457i
$195$	−33774.3	−	58498.8i	−0.0636063	−	0.110169i
$196$	133514.	−	231253.i	0.248249	−	0.429980i
$197$	−762522.			−1.39987			−0.699934	−	0.714208i	$-0.746787\pi$
$197$	−762522.			−1.39987			−0.699934	+	0.714208i	$0.746787\pi$
$198$	31502.1			0.0571054
$199$	204567.	−	354320.i	0.366186	−	0.634254i	−0.622779	−	0.782398i	$-0.713997\pi$
$199$	204567.	−	354320.i	0.366186	−	0.634254i	0.988966	+	0.148144i	$0.0473299\pi$
$200$	−74391.4	+	128850.i	−0.131507	+	0.227776i
$201$	1.27096e6			2.21892
$202$	−420245.			−0.724644
$203$	−17773.9	+	30785.3i	−0.0302721	+	0.0524329i
$204$	−70231.7	−	121645.i	−0.118156	−	0.204653i
$205$	54520.7	−	94432.7i	0.0906102	−	0.156941i
$206$	−83301.1	−	144282.i	−0.136767	−	0.236888i
$207$	56925.2	+	98597.4i	0.0923377	+	0.159934i
$208$	33426.1			0.0535706
$209$	−100886.	−	90515.9i	−0.159760	−	0.143337i
$210$	22452.6			0.0351333
$211$	612069.	+	1.06013e6i	0.946442	+	1.63929i	0.752838	+	0.658206i	$0.228685\pi$
$211$	612069.	+	1.06013e6i	0.946442	+	1.63929i	0.193604	+	0.981080i	$0.437982\pi$
$212$	−233343.	−	404163.i	−0.356579	−	0.617613i
$213$	542602.	−	939815.i	0.819469	−	1.41936i
$214$	211516.	+	366357.i	0.315725	+	0.546852i
$215$	−12830.9	+	22223.7i	−0.0189304	+	0.0327884i
$216$	−177396.			−0.258707
$217$	−63182.6			−0.0910853
$218$	425289.	−	736623.i	0.606098	−	1.04979i
$219$	328023.	−	568153.i	0.462162	−	0.800488i
$220$	38987.3			0.0543083
$221$	−62680.8			−0.0863285
$222$	46998.8	−	81404.2i	0.0640035	−	0.110857i
$223$	−4819.97	−	8348.43i	−0.00649056	−	0.0112420i	0.862762	−	0.505610i	$-0.168733\pi$
$223$	−4819.97	−	8348.43i	−0.00649056	−	0.0112420i	−0.869252	+	0.494368i	$0.835399\pi$
$224$	−5555.27	+	9622.02i	−0.00739751	+	0.0128129i
$225$	106277.	+	184077.i	0.139953	+	0.242405i
$226$	−11870.2	−	20559.8i	−0.0154592	−	0.0267762i
$227$	−1.10737e6			−1.42635			−0.713177	−	0.700984i	$-0.752745\pi$
$227$	−1.10737e6			−1.42635			−0.713177	+	0.700984i	$0.752745\pi$
$228$	−342706.	−	307478.i	−0.436601	−	0.391721i
$229$	215081.			0.271027			0.135514	−	0.990775i	$-0.456732\pi$
$229$	215081.			0.271027			0.135514	+	0.990775i	$0.456732\pi$
$230$	70451.1	+	122025.i	0.0878149	+	0.152100i
$231$	8545.63	+	14801.5i	0.0105369	+	0.0182505i
$232$	−104840.	+	181588.i	−0.127881	+	0.221497i
$233$	40346.0	+	69881.4i	0.0486868	+	0.0843280i	0.889342	−	0.457243i	$-0.151163\pi$
$233$	40346.0	+	69881.4i	0.0486868	+	0.0843280i	−0.840655	+	0.541571i	$0.817830\pi$
$234$	23876.5	−	41355.3i	0.0285056	−	0.0493732i
$235$	−303412.			−0.358396
$236$	152159.			0.177835
$237$	897870.	−	1.55516e6i	1.03835	−	1.79847i
$238$	10417.3	−	18043.3i	0.0119210	−	0.0206478i
$239$	570997.			0.646606			0.323303	−	0.946296i	$-0.395207\pi$
$239$	570997.			0.646606			0.323303	+	0.946296i	$0.395207\pi$
$240$	132438.			0.148417
$241$	68090.9	−	117937.i	0.0755173	−	0.130800i	−0.825794	−	0.563972i	$-0.809273\pi$
$241$	68090.9	−	117937.i	0.0755173	−	0.130800i	0.901311	+	0.433172i	$0.142606\pi$
$242$	−307263.	−	532195.i	−0.337266	−	0.584161i
$243$	−329869.	+	571349.i	−0.358365	+	0.620706i
$244$	11045.5	+	19131.3i	0.0118771	+	0.0205717i
$245$	−236062.	−	408871.i	−0.251252	−	0.435182i
$246$	281960.			0.297064
$247$	−195292.	+	63836.5i	−0.203677	+	0.0665774i
$248$	−372685.			−0.384780
$249$	418868.	+	725501.i	0.428133	+	0.741549i
$250$	308335.	+	534052.i	0.312013	+	0.540423i
$251$	9154.96	−	15856.9i	0.00917218	−	0.0158867i	−0.861403	−	0.507922i	$-0.830414\pi$
$251$	9154.96	−	15856.9i	0.00917218	−	0.0158867i	0.870575	+	0.492036i	$0.163747\pi$
$252$	7936.35	+	13746.2i	0.00787262	+	0.0136358i
$253$	−53628.4	+	92887.1i	−0.0526736	+	0.0912334i
$254$	294951.			0.286857
$255$	−248348.			−0.239172
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	202885.	−	351407.i	0.191610	−	0.331878i	−0.754174	−	0.656674i	$-0.771963\pi$
$257$	202885.	−	351407.i	0.191610	−	0.331878i	0.945784	+	0.324797i	$0.105296\pi$
$258$	−66356.1			−0.0620628
$259$	13942.4			0.0129148
$260$	29549.7	−	51181.6i	0.0271094	−	0.0469548i
$261$	149776.	+	259420.i	0.136095	+	0.235723i
$262$	−641483.	+	1.11108e6i	−0.577341	+	0.999983i
$263$	238596.	+	413260.i	0.212703	+	0.368412i	0.952560	−	0.304352i	$-0.0984400\pi$
$263$	238596.	+	413260.i	0.212703	+	0.368412i	−0.739857	+	0.672765i	$0.765107\pi$
$264$	50406.7	+	87307.0i	0.0445121	+	0.0770973i
$265$	−825133.			−0.721787
$266$	14080.8	−	66826.2i	0.0122018	−	0.0579085i
$267$	−1.70928e6			−1.46736
$268$	555992.	+	963007.i	0.472859	+	0.819016i
$269$	−1.00942e6	−	1.74836e6i	−0.850530	−	1.47316i	−0.880730	−	0.473618i	$-0.842948\pi$
$269$	−1.00942e6	−	1.74836e6i	−0.850530	−	1.47316i	0.0301999	−	0.999544i	$-0.490386\pi$
$270$	−156823.	+	271626.i	−0.130919	+	0.226758i
$271$	1.12882e6	+	1.95518e6i	0.933691	+	1.61720i	0.776951	+	0.629561i	$0.216765\pi$
$271$	1.12882e6	+	1.95518e6i	0.933691	+	1.61720i	0.156740	+	0.987640i	$0.449902\pi$
$272$	61446.8	−	106429.i	0.0503590	−	0.0872244i
$273$	25908.0			0.0210391
$274$	42417.4			0.0341325
$275$	−100122.	+	173416.i	−0.0798355	+	0.138279i
$276$	−182173.	+	315532.i	−0.143950	+	0.249328i
$277$	209784.			0.164276			0.0821379	−	0.996621i	$-0.473825\pi$
$277$	209784.			0.164276			0.0821379	+	0.996621i	$0.473825\pi$
$278$	665469.			0.516435
$279$	−266212.	+	461092.i	−0.204747	+	0.354632i
$280$	9822.08	+	17012.3i	0.00748701	+	0.0129679i
$281$	−1.13653e6	+	1.96852e6i	−0.858644	+	1.48722i	0.0145782	+	0.999894i	$0.495359\pi$
$281$	−1.13653e6	+	1.96852e6i	−0.858644	+	1.48722i	−0.873222	+	0.487322i	$0.837974\pi$
$282$	−392282.	−	679453.i	−0.293749	−	0.508788i
$283$	277763.	+	481100.i	0.206162	+	0.357083i	0.950502	−	0.310718i	$-0.100569\pi$
$283$	277763.	+	481100.i	0.206162	+	0.357083i	−0.744340	+	0.667800i	$0.767236\pi$
$284$	949463.			0.698526
$285$	−773769.	+	252927.i	−0.564286	+	0.184452i
$286$	44987.3			0.0325218
$287$	20911.2	+	36219.3i	0.0149856	+	0.0259558i
$288$	46812.8	+	81082.2i	0.0332571	+	0.0576029i
$289$	594703.	−	1.03006e6i	0.418847	−	0.725464i
$290$	185364.	+	321060.i	0.129429	+	0.224177i
$291$	−249696.	+	432485.i	−0.172854	+	0.299391i
$292$	573986.			0.393953
$293$	−1.03492e6			−0.704266			−0.352133	−	0.935950i	$-0.614544\pi$
$293$	−1.03492e6			−0.704266			−0.352133	+	0.935950i	$0.614544\pi$
$294$	610409.	−	1.05726e6i	0.411863	−	0.713367i
$295$	134513.	−	232984.i	0.0899933	−	0.155873i
$296$	82240.0			0.0545574
$297$	−238752.			−0.157057
$298$	396567.	−	686873.i	0.258688	−	0.448060i
$299$	81293.3	+	140804.i	0.0525868	+	0.0910830i
$300$	−340107.	+	589083.i	−0.218179	+	0.377897i
$301$	−4921.22	−	8523.81i	−0.00313081	−	0.00542272i
$302$	−302191.	−	523411.i	−0.190662	−	0.330237i
$303$	−1.92131e6			−1.20224
$304$	83056.3	−	394177.i	0.0515452	−	0.244628i
$305$	39058.2			0.0240416
$306$	−87783.8	−	152046.i	−0.0535934	−	0.0928264i
$307$	−1.30526e6	−	2.26078e6i	−0.790409	−	1.36903i	−0.925714	−	0.378225i	$-0.876535\pi$
$307$	−1.30526e6	−	2.26078e6i	−0.790409	−	1.36903i	0.135304	−	0.990804i	$-0.456799\pi$
$308$	−7476.71	+	12950.0i	−0.00449090	+	0.00777847i
$309$	−380842.	−	659637.i	−0.226907	−	0.393015i
$310$	−329466.	+	570651.i	−0.194718	+	0.337261i
$311$	1.29605e6			0.759838			0.379919	−	0.925020i	$-0.375952\pi$
$311$	1.29605e6			0.759838			0.379919	+	0.925020i	$0.375952\pi$
$312$	152819.			0.0888775
$313$	8751.09	−	15157.3i	0.00504895	−	0.00874504i	−0.863490	−	0.504366i	$-0.831726\pi$
$313$	8751.09	−	15157.3i	0.00504895	−	0.00874504i	0.868539	+	0.495621i	$0.165060\pi$
$314$	818704.	−	1.41804e6i	0.468600	−	0.811640i
$315$	28063.9			0.0159357
$316$	1.57112e6			0.885100
$317$	1.35753e6	−	2.35132e6i	0.758757	−	1.31421i	−0.184728	−	0.982790i	$-0.559140\pi$
$317$	1.35753e6	−	2.35132e6i	0.758757	−	1.31421i	0.943485	−	0.331415i	$-0.107526\pi$
$318$	−1.06682e6	−	1.84778e6i	−0.591591	−	1.02467i
$319$	−141102.	+	244395.i	−0.0776347	+	0.134467i
$320$	57935.9	+	100348.i	0.0316281	+	0.0547815i
$321$	967025.	+	1.67494e6i	0.523811	+	0.907268i
$322$	−54042.5			−0.0290466
$323$	−155748.	+	739164.i	−0.0830645	+	0.394216i
$324$	−1.16651e6			−0.617344
$325$	151771.	+	262874.i	0.0797039	+	0.138051i
$326$	910958.	+	1.57783e6i	0.474739	+	0.822271i
$327$	1.94437e6	−	3.36774e6i	1.00556	−	1.74168i
$328$	123346.	+	213641.i	0.0633052	+	0.109648i
$329$	58186.3	−	100782.i	0.0296368	−	0.0513324i
$330$	178245.			0.0901014
$331$	1.31224e6			0.658329			0.329165	−	0.944273i	$-0.393233\pi$
$331$	1.31224e6			0.658329			0.329165	+	0.944273i	$0.393233\pi$
$332$	−366475.	+	634753.i	−0.182473	+	0.316053i
$333$	58744.6	−	101749.i	0.0290307	−	0.0502826i
$334$	−932730.			−0.457499
$335$	1.96606e6			0.957161
$336$	−25398.0	+	43990.6i	−0.0122730	+	0.0212575i
$337$	835316.	+	1.44681e6i	0.400660	+	0.693963i	0.993806	−	0.111132i	$-0.0354476\pi$
$337$	835316.	+	1.44681e6i	0.400660	+	0.693963i	−0.593146	+	0.805095i	$0.702114\pi$
$338$	−708489.	+	1.22714e6i	−0.337319	+	0.584254i
$339$	−54269.1	−	93996.8i	−0.0256480	−	0.0444236i
$340$	−108642.	−	188173.i	−0.0509683	−	0.0882797i
$341$	−501588.			−0.233594
$342$	−428354.	−	384322.i	−0.198033	−	0.177676i
$343$	363439.			0.166800
$344$	−29028.0	−	50278.0i	−0.0132258	−	0.0229077i
$345$	322093.	+	557881.i	0.145691	+	0.252345i
$346$	−1.19055e6	+	2.06208e6i	−0.534633	+	0.926011i
$347$	681995.	+	1.18125e6i	0.304059	+	0.526645i	0.977051	−	0.213004i	$-0.0683247\pi$
$347$	681995.	+	1.18125e6i	0.304059	+	0.526645i	−0.672992	+	0.739649i	$0.734991\pi$
$348$	−479315.	+	830198.i	−0.212165	+	0.367480i
$349$	498862.			0.219238			0.109619	−	0.993974i	$-0.465037\pi$
$349$	498862.			0.219238			0.109619	+	0.993974i	$0.465037\pi$
$350$	−100895.			−0.0440249
$351$	−180958.	+	313429.i	−0.0783989	+	0.135791i
$352$	−44101.7	+	76386.3i	−0.0189713	+	0.0328593i
$353$	391339.			0.167154			0.0835770	−	0.996501i	$-0.473366\pi$
$353$	391339.			0.167154			0.0835770	+	0.996501i	$0.473366\pi$
$354$	695650.			0.295041
$355$	839356.	−	1.45381e6i	0.353489	−	0.612260i
$356$	−747741.	−	1.29512e6i	−0.312699	−	0.541610i
$357$	47626.5	−	82491.5i	0.0197778	−	0.0342562i
$358$	−904243.	−	1.56620e6i	−0.372887	−	0.645860i
$359$	305778.	+	529622.i	0.125219	+	0.216885i	0.921818	−	0.387622i	$-0.126703\pi$
$359$	305778.	+	529622.i	0.125219	+	0.216885i	−0.796600	+	0.604507i	$0.793370\pi$
$360$	165536.			0.0673189
$361$	267534.	+	2.46160e6i	0.108047	+	0.994146i
$362$	−374113.			−0.150049
$363$	−1.40477e6	−	2.43313e6i	−0.559548	−	0.969166i
$364$	11333.7	+	19630.5i	0.00448350	+	0.00776565i
$365$	507422.	−	878881.i	0.199360	−	0.345301i
$366$	50498.4	+	87465.8i	0.0197049	+	0.0341299i
$367$	1.29534e6	−	2.24359e6i	0.502017	−	0.869519i	−0.497980	−	0.867188i	$-0.665925\pi$
$367$	1.29534e6	−	2.24359e6i	0.502017	−	0.869519i	0.999997	−	0.00233081i	$-0.000741920\pi$
$368$	−318772.			−0.122704
$369$	352427.			0.134742
$370$	72702.8	−	125925.i	0.0276087	−	0.0478197i
$371$	158238.	−	274077.i	0.0596865	−	0.103380i
$372$	−1.70387e6			−0.638379
$373$	−3.40478e6			−1.26712			−0.633560	−	0.773694i	$-0.718407\pi$
$373$	−3.40478e6			−1.26712			−0.633560	+	0.773694i	$0.718407\pi$
$374$	82699.8	−	143240.i	0.0305721	−	0.0529525i
$375$	1.40967e6	+	2.44162e6i	0.517653	+	0.896601i
$376$	343214.	−	594464.i	0.125197	−	0.216848i
$377$	213891.	+	370470.i	0.0775067	+	0.134246i
$378$	−60149.0	−	104181.i	−0.0216520	−	0.0375024i
$379$	−3.76526e6			−1.34647			−0.673236	−	0.739428i	$-0.735096\pi$
$379$	−3.76526e6			−1.34647			−0.673236	+	0.739428i	$0.735096\pi$
$380$	−530135.	−	475640.i	−0.188333	−	0.168974i
$381$	1.34848e6			0.475917
$382$	−272022.	−	471156.i	−0.0953774	−	0.165199i
$383$	−1.05985e6	−	1.83572e6i	−0.369190	−	0.639455i	0.620250	−	0.784405i	$-0.287031\pi$
$383$	−1.05985e6	−	1.83572e6i	−0.369190	−	0.639455i	−0.989439	+	0.144950i	$0.953698\pi$
$384$	−149811.	+	259480.i	−0.0518460	+	0.0897999i
$385$	13219.3	+	22896.5i	0.00454524	+	0.00787258i
$386$	−735162.	+	1.27334e6i	−0.251139	+	0.434986i
$387$	−82939.7			−0.0281504
$388$	−436925.			−0.147342
$389$	−1.99533e6	+	3.45602e6i	−0.668561	+	1.15798i	0.309745	+	0.950820i	$0.399756\pi$
$389$	−1.99533e6	+	3.45602e6i	−0.668561	+	1.15798i	−0.978307	+	0.207163i	$0.933577\pi$
$390$	135097.	−	233995.i	0.0449764	−	0.0779015i
$391$	597763.			0.197737
$392$	1.06811e6			0.351077
$393$	−2.93278e6	+	5.07972e6i	−0.957850	+	1.65904i
$394$	−1.52504e6	−	2.64145e6i	−0.494928	−	0.857240i
$395$	1.38892e6	−	2.40569e6i	0.447905	−	0.775793i
$396$	63004.3	+	109127.i	0.0201898	+	0.0349698i
$397$	−998280.	−	1.72907e6i	−0.317890	−	0.550601i	0.662158	−	0.749364i	$-0.269641\pi$
$397$	−998280.	−	1.72907e6i	−0.317890	−	0.550601i	−0.980047	+	0.198763i	$0.936307\pi$
$398$	1.63653e6			0.517866
$399$	64375.6	−	305520.i	0.0202437	−	0.0960744i
$400$	−595131.			−0.185978
$401$	1.52421e6	+	2.64001e6i	0.473352	+	0.819870i	0.999535	−	0.0305014i	$-0.00971041\pi$
$401$	1.52421e6	+	2.64001e6i	0.473352	+	0.819870i	−0.526182	+	0.850372i	$0.676377\pi$
$402$	2.54192e6	+	4.40274e6i	0.784508	+	1.35881i
$403$	−380170.	+	658473.i	−0.116604	+	0.201965i
$404$	−840491.	−	1.45577e6i	−0.256200	−	0.443752i
$405$	−1.03124e6	+	1.78615e6i	−0.312407	+	0.541104i
$406$	−142191.			−0.0428113
$407$	110685.			0.0331209
$408$	280927.	−	486579.i	0.0835493	−	0.144712i
$409$	−2.58130e6	+	4.47094e6i	−0.763010	+	1.32157i	0.178283	+	0.983979i	$0.442946\pi$
$409$	−2.58130e6	+	4.47094e6i	−0.763010	+	1.32157i	−0.941292	+	0.337592i	$0.890388\pi$
$410$	436166.			0.128142
$411$	193927.			0.0566282
$412$	333205.	−	577127.i	0.0967092	−	0.167505i
$413$	51592.0	+	89360.0i	0.0148836	+	0.0257791i
$414$	−227701.	+	394390.i	−0.0652926	+	0.113090i
$415$	647951.	+	1.12228e6i	0.184681	+	0.319877i
$416$	66852.1	+	115791.i	0.0189401	+	0.0328052i
$417$	3.04243e6			0.856803
$418$	111783.	−	530513.i	0.0312922	−	0.148510i
$419$	2.10626e6			0.586106			0.293053	−	0.956096i	$-0.405329\pi$
$419$	2.10626e6			0.586106			0.293053	+	0.956096i	$0.405329\pi$
$420$	44905.2	+	77778.2i	0.0124215	+	0.0215147i
$421$	−1.10606e6	−	1.91576e6i	−0.304141	−	0.526788i	0.672929	−	0.739707i	$-0.265036\pi$
$421$	−1.10606e6	−	1.91576e6i	−0.304141	−	0.526788i	−0.977070	+	0.212920i	$0.931703\pi$
$422$	−2.44828e6	+	4.24054e6i	−0.669236	+	1.15915i
$423$	−490321.	−	849260.i	−0.133238	−	0.230776i
$424$	933374.	−	1.61665e6i	0.252140	−	0.436719i
$425$	1.11599e6			0.299702
$426$	4.34082e6			1.15890
$427$	−7490.31	+	12973.6i	−0.00198806	+	0.00344343i
$428$	−846066.	+	1.46543e6i	−0.223252	+	0.386683i
$429$	205676.			0.0539561
$430$	−102647.			−0.0267716
$431$	−1.18735e6	+	2.05655e6i	−0.307883	+	0.533269i	−0.977899	−	0.209077i	$-0.932954\pi$
$431$	−1.18735e6	+	2.05655e6i	−0.307883	+	0.533269i	0.670016	+	0.742347i	$0.266287\pi$
$432$	−354791.	−	614516.i	−0.0914668	−	0.158425i
$433$	2.76130e6	−	4.78271e6i	0.707773	−	1.22590i	−0.257908	−	0.966169i	$-0.583033\pi$
$433$	2.76130e6	−	4.78271e6i	0.707773	−	1.22590i	0.965681	−	0.259729i	$-0.0836334\pi$
$434$	−126365.	−	218871.i	−0.0322035	−	0.0557781i
$435$	847460.	+	1.46784e6i	0.214732	+	0.371926i
$436$	3.40231e6			0.857153
$437$	1.86243e6	−	608785.i	0.466526	−	0.152497i
$438$	2.62419e6			0.653596
$439$	−3.16832e6	−	5.48769e6i	−0.784634	−	1.35903i	−0.929217	−	0.369534i	$-0.879517\pi$
$439$	−3.16832e6	−	5.48769e6i	−0.784634	−	1.35903i	0.144583	−	0.989493i	$-0.453816\pi$
$440$	77974.6	+	135056.i	0.0192009	+	0.0332569i
$441$	762961.	−	1.32149e6i	0.186813	−	0.323569i
$442$	−125362.	−	217133.i	−0.0305217	−	0.0528652i
$443$	2.01937e6	−	3.49765e6i	0.488885	−	0.846774i	−0.511033	−	0.859561i	$-0.670737\pi$
$443$	2.01937e6	−	3.49765e6i	0.488885	−	0.846774i	0.999918	+	0.0127871i	$0.00407037\pi$
$444$	375990.			0.0905147
$445$	−2.64411e6			−0.632964
$446$	19279.9	−	33393.7i	0.00458952	−	0.00794928i
$447$	1.81305e6	−	3.14029e6i	0.429181	−	0.743364i
$448$	−44442.2			−0.0104617
$449$	−6.51972e6			−1.52621			−0.763103	−	0.646277i	$-0.776325\pi$
$449$	−6.51972e6			−1.52621			−0.763103	+	0.646277i	$0.776325\pi$
$450$	−425106.	+	736306.i	−0.0989615	+	0.171406i
$451$	166008.	+	287534.i	0.0384315	+	0.0665653i
$452$	47480.9	−	82239.3i	0.0109313	−	0.0189336i
$453$	−1.38158e6	−	2.39296e6i	−0.316323	−	0.547887i
$454$	−2.21474e6	−	3.83604e6i	−0.504293	−	0.873460i
$455$	40077.3			0.00907549
$456$	379722.	−	1.80212e6i	0.0855173	−	0.405856i
$457$	3.89603e6			0.872633			0.436316	−	0.899793i	$-0.356283\pi$
$457$	3.89603e6			0.872633			0.436316	+	0.899793i	$0.356283\pi$
$458$	430162.	+	745062.i	0.0958226	+	0.165970i
$459$	665308.	+	1.15235e6i	0.147398	+	0.255300i
$460$	−281804.	+	488100.i	−0.0620945	+	0.107551i
$461$	−3.93218e6	−	6.81073e6i	−0.861749	−	1.49259i	−0.870239	−	0.492629i	$-0.836036\pi$
$461$	−3.93218e6	−	6.81073e6i	−0.861749	−	1.49259i	0.00849019	−	0.999964i	$-0.497297\pi$
$462$	−34182.5	+	59205.8i	−0.00745073	+	0.0129050i
$463$	−4.54224e6			−0.984731			−0.492365	−	0.870389i	$-0.663868\pi$
$463$	−4.54224e6			−0.984731			−0.492365	+	0.870389i	$0.663868\pi$
$464$	−838721.			−0.180852
$465$	−1.50627e6	+	2.60894e6i	−0.323051	+	0.559541i
$466$	−161384.	+	279526.i	−0.0344268	+	0.0596289i
$467$	2.08247e6			0.441861			0.220930	−	0.975290i	$-0.429091\pi$
$467$	2.08247e6			0.441861			0.220930	+	0.975290i	$0.429091\pi$
$468$	191012.			0.0403130
$469$	−377037.	+	653048.i	−0.0791503	+	0.137092i
$470$	−606825.	−	1.05105e6i	−0.126712	−	0.219472i
$471$	3.74300e6	−	6.48307e6i	0.777442	−	1.34657i
$472$	304318.	+	527094.i	0.0628742	+	0.108901i
$473$	−39068.1	−	67667.9i	−0.00802915	−	0.0139069i
$474$	7.18296e6			1.46845
$475$	3.47706e6	−	1.13657e6i	0.707096	−	0.231133i
$476$	83338.4			0.0168588
$477$	−1.33343e6	−	2.30957e6i	−0.268333	−	0.464767i
$478$	1.14199e6	+	1.97799e6i	0.228610	+	0.395963i
$479$	−3.24654e6	+	5.62317e6i	−0.646519	+	1.11980i	0.337429	+	0.941351i	$0.390443\pi$
$479$	−3.24654e6	+	5.62317e6i	−0.646519	+	1.11980i	−0.983948	+	0.178454i	$0.942891\pi$
$480$	264875.	+	458778.i	0.0524733	+	0.0908864i
$481$	83891.5	−	145304.i	0.0165331	−	0.0286362i
$482$	544727.			0.106798
$483$	−247075.			−0.0481904
$484$	1.22905e6	−	2.12878e6i	0.238483	−	0.413064i
$485$	−386256.	+	669015.i	−0.0745626	+	0.129146i
$486$	−2.63895e6			−0.506804
$487$	−2.50898e6			−0.479375			−0.239687	−	0.970850i	$-0.577045\pi$
$487$	−2.50898e6			−0.479375			−0.239687	+	0.970850i	$0.577045\pi$
$488$	−44181.9	+	76525.3i	−0.00839836	+	0.0145464i
$489$	4.16478e6	+	7.21361e6i	0.787626	+	1.36421i
$490$	944247.	−	1.63548e6i	0.177662	−	0.307720i
$491$	3.75831e6	+	6.50958e6i	0.703540	+	1.21857i	0.967216	+	0.253955i	$0.0817316\pi$
$491$	3.75831e6	+	6.50958e6i	0.703540	+	1.21857i	−0.263676	+	0.964611i	$0.584935\pi$
$492$	563920.	+	976737.i	0.105028	+	0.181914i
$493$	1.57278e6			0.291440
$494$	−611721.	−	548839.i	−0.112781	−	0.101188i
$495$	222791.			0.0408682
$496$	−745370.	−	1.29102e6i	−0.136040	−	0.235629i
$497$	321932.	+	557602.i	0.0584619	+	0.101259i
$498$	−1.67547e6	+	2.90201e6i	−0.302736	+	0.524354i
$499$	311806.	+	540063.i	0.0560573	+	0.0970941i	0.892692	−	0.450667i	$-0.148814\pi$
$499$	311806.	+	540063.i	0.0560573	+	0.0970941i	−0.836635	+	0.547761i	$0.815480\pi$
$500$	−1.23334e6	+	2.13621e6i	−0.220627	+	0.382137i
$501$	−4.26432e6			−0.759023
$502$	73239.7			0.0129714
$503$	−3.38840e6	+	5.86887e6i	−0.597137	+	1.03427i	0.396104	+	0.918206i	$0.370362\pi$
$503$	−3.38840e6	+	5.86887e6i	−0.597137	+	1.03427i	−0.993241	+	0.116066i	$0.962971\pi$
$504$	−31745.4	+	54984.6i	−0.00556678	+	0.00964195i
$505$	−2.97208e6			−0.518600
$506$	−429027.			−0.0744918
$507$	−3.23912e6	+	5.61031e6i	−0.559637	+	0.969320i
$508$	589902.	+	1.02174e6i	0.101419	+	0.175663i
$509$	4.70543e6	−	8.15005e6i	0.805017	−	1.39433i	−0.111263	−	0.993791i	$-0.535489\pi$
$509$	4.70543e6	−	8.15005e6i	0.805017	−	1.39433i	0.916280	−	0.400539i	$-0.131177\pi$
$510$	−496696.	−	860304.i	−0.0845601	−	0.146462i
$511$	194620.	+	337091.i	0.0329712	+	0.0571077i
$512$	−262144.			−0.0441942
$513$	3.24647e6	+	2.91275e6i	0.544650	+	0.488663i
$514$	1.62308e6			0.270977
$515$	−589127.	−	1.02040e6i	−0.0978793	−	0.169532i
$516$	−132712.	−	229864.i	−0.0219425	−	0.0380056i
$517$	461924.	−	800075.i	0.0760053	−	0.131645i
$518$	27884.9	+	48298.0i	0.00456609	+	0.00790869i
$519$	−5.44301e6	+	9.42757e6i	−0.886995	+	1.53632i
$520$	236398.			0.0383385
$521$	−4.87226e6			−0.786387			−0.393194	−	0.919456i	$-0.628630\pi$
$521$	−4.87226e6			−0.786387			−0.393194	+	0.919456i	$0.628630\pi$
$522$	−599104.	+	1.03768e6i	−0.0962335	+	0.166681i
$523$	1.03700e6	−	1.79614e6i	0.165778	−	0.287135i	−0.771153	−	0.636649i	$-0.780320\pi$
$523$	1.03700e6	−	1.79614e6i	0.165778	−	0.287135i	0.936931	+	0.349514i	$0.113653\pi$
$524$	−5.13187e6			−0.816483
$525$	−461277.			−0.0730404
$526$	−954383.	+	1.65304e6i	−0.150404	+	0.260507i
$527$	1.39773e6	+	2.42093e6i	0.219228	+	0.379713i
$528$	−201627.	+	349228.i	−0.0314748	+	0.0545160i
$529$	2.44291e6	+	4.23124e6i	0.379549	+	0.657398i
$530$	−1.65027e6	−	2.85834e6i	−0.255190	−	0.442002i
$531$	869505.			0.133825
$532$	259654.	−	84874.9i	0.0397756	−	0.0130017i
$533$	503291.			0.0767363
$534$	−3.41857e6	−	5.92114e6i	−0.518790	−	0.898570i
$535$	1.49590e6	+	2.59097e6i	0.225953	+	0.391362i
$536$	−2.22397e6	+	3.85203e6i	−0.334362	+	0.579132i
$537$	−4.13408e6	−	7.16044e6i	−0.618647	−	1.07153i
$538$	4.03767e6	−	6.99345e6i	0.601416	−	1.04168i
$539$	1.43755e6			0.213133
$540$	−1.25459e6			−0.185147
$541$	−1.19724e6	+	2.07368e6i	−0.175868	+	0.304613i	−0.940461	−	0.339900i	$-0.889607\pi$
$541$	−1.19724e6	+	2.07368e6i	−0.175868	+	0.304613i	0.764593	+	0.644513i	$0.222940\pi$
$542$	−4.51530e6	+	7.82073e6i	−0.660219	+	1.14353i
$543$	−1.71040e6			−0.248941
$544$	491575.			0.0712184
$545$	3.00776e6	−	5.20959e6i	0.433762	−	0.751297i
$546$	51816.0	+	89748.0i	0.00743845	+	0.0128838i
$547$	3.33054e6	−	5.76866e6i	0.475933	−	0.824341i	−0.523687	−	0.851911i	$-0.675444\pi$
$547$	3.33054e6	−	5.76866e6i	0.475933	−	0.824341i	0.999620	+	0.0275703i	$0.00877702\pi$
$548$	84834.8	+	146938.i	0.0120676	+	0.0209018i
$549$	63118.9	+	109325.i	0.00893775	+	0.0154806i
$550$	−800972.			−0.112904
$551$	4.90024e6	−	1.60177e6i	0.687604	−	0.224762i
$552$	−1.45738e6			−0.203575
$553$	532716.	+	922691.i	0.0740769	+	0.128305i
$554$	419568.	+	726714.i	0.0580802	+	0.100598i
$555$	332387.	−	575712.i	0.0458049	−	0.0793364i
$556$	1.33094e6	+	2.30525e6i	0.182587	+	0.316251i
$557$	644989.	−	1.11715e6i	0.0880875	−	0.152572i	−0.818615	−	0.574342i	$-0.805258\pi$
$557$	644989.	−	1.11715e6i	0.0880875	−	0.152572i	0.906703	+	0.421770i	$0.138591\pi$
$558$	−2.12969e6			−0.289555
$559$	−118444.			−0.0160318
$560$	−39288.3	+	68049.4i	−0.00529412	+	0.00916968i
$561$	378092.	−	654875.i	0.0507213	−	0.0878520i
$562$	−9.09220e6			−1.21431
$563$	6.62220e6			0.880503			0.440252	−	0.897874i	$-0.354889\pi$
$563$	6.62220e6			0.880503			0.440252	+	0.897874i	$0.354889\pi$
$564$	1.56913e6	−	2.71781e6i	0.207712	−	0.359767i
$565$	−83949.3	−	145404.i	−0.0110636	−	0.0191627i
$566$	−1.11105e6	+	1.92440e6i	−0.145778	+	0.252496i
$567$	−395526.	−	685072.i	−0.0516675	−	0.0894908i
$568$	1.89893e6	+	3.28904e6i	0.246966	+	0.427758i
$569$	1.15720e7			1.49840			0.749201	−	0.662342i	$-0.230438\pi$
$569$	1.15720e7			1.49840			0.749201	+	0.662342i	$0.230438\pi$
$570$	−2.42370e6	−	2.17456e6i	−0.312459	−	0.280340i
$571$	−6.94664e6			−0.891629			−0.445815	−	0.895125i	$-0.647086\pi$
$571$	−6.94664e6			−0.891629			−0.445815	+	0.895125i	$0.647086\pi$
$572$	89974.6	+	155841.i	0.0114982	+	0.0199155i
$573$	−1.24365e6	−	2.15406e6i	−0.158238	−	0.274076i
$574$	−83644.9	+	144877.i	−0.0105964	+	0.0183536i
$575$	−1.44738e6	−	2.50693e6i	−0.182563	−	0.316208i
$576$	−187251.	+	324329.i	−0.0235163	+	0.0407314i
$577$	1.12482e7			1.40651			0.703255	−	0.710937i	$-0.251729\pi$
$577$	1.12482e7			1.40651			0.703255	+	0.710937i	$0.251729\pi$
$578$	4.75762e6			0.592339
$579$	−3.36106e6	+	5.82153e6i	−0.416658	+	0.721673i
$580$	−741456.	+	1.28424e6i	−0.0915199	+	0.158517i
$581$	−497038.			−0.0610871
$582$	−1.99756e6			−0.244452
$583$	1.25621e6	−	2.17581e6i	0.153070	−	0.265124i
$584$	1.14797e6	+	1.98835e6i	0.139283	+	0.241246i
$585$	168861.	−	292475.i	0.0204004	−	0.0353345i
$586$	−2.06984e6	−	3.58506e6i	−0.248996	−	0.431273i
$587$	−995272.	−	1.72386e6i	−0.119219	−	0.206494i	0.800239	−	0.599681i	$-0.204706\pi$
$587$	−995272.	−	1.72386e6i	−0.119219	−	0.206494i	−0.919459	+	0.393187i	$0.871372\pi$
$588$	4.88327e6			0.582462
$589$	6.82041e6	+	6.11931e6i	0.810069	+	0.726798i
$590$	1.07611e6			0.127270
$591$	−6.97230e6	−	1.20764e7i	−0.821121	−	1.42222i
$592$	164480.	+	284888.i	0.0192889	+	0.0334094i
$593$	5.81327e6	−	1.00689e7i	0.678866	−	1.17583i	−0.296457	−	0.955046i	$-0.595805\pi$
$593$	5.81327e6	−	1.00689e7i	0.678866	−	1.17583i	0.975323	−	0.220784i	$-0.0708615\pi$
$594$	−477505.	−	827063.i	−0.0555280	−	0.0961772i
$595$	73673.8	−	127607.i	0.00853141	−	0.0147768i
$596$	3.17253e6			0.365839
$597$	7.48201e6			0.859177
$598$	−325173.	+	563217.i	−0.0371845	+	0.0644054i
$599$	2.02259e6	−	3.50324e6i	0.230325	−	0.398935i	−0.727578	−	0.686024i	$-0.759354\pi$
$599$	2.02259e6	−	3.50324e6i	0.230325	−	0.398935i	0.957904	+	0.287089i	$0.0926876\pi$
$600$	−2.72086e6			−0.308552
$601$	−2.58476e6			−0.291900			−0.145950	−	0.989292i	$-0.546624\pi$
$601$	−2.58476e6			−0.291900			−0.145950	+	0.989292i	$0.546624\pi$
$602$	19684.9	−	34095.2i	0.00221382	−	0.00383444i
$603$	3.17720e6	+	5.50306e6i	0.355837	+	0.616327i
$604$	1.20877e6	−	2.09364e6i	0.134819	−	0.233513i
$605$	−2.17304e6	−	3.76382e6i	−0.241368	−	0.418062i
$606$	−3.84261e6	−	6.65560e6i	−0.425055	−	0.736216i
$607$	−1.07630e7			−1.18567			−0.592833	−	0.805325i	$-0.701991\pi$
$607$	−1.07630e7			−1.18567			−0.592833	+	0.805325i	$0.701991\pi$
$608$	1.53158e6	−	500638.i	0.168028	−	0.0549244i
$609$	−650080.			−0.0710270
$610$	78116.4	+	135302.i	0.00849998	+	0.0147224i
$611$	−700213.	−	1.21280e6i	−0.0758800	−	0.131428i
$612$	351135.	−	608184.i	0.0378962	−	0.0656382i
$613$	461938.	+	800100.i	0.0496515	+	0.0859989i	0.889783	−	0.456384i	$-0.150856\pi$
$613$	461938.	+	800100.i	0.0496515	+	0.0859989i	−0.840132	+	0.542383i	$0.817522\pi$
$614$	5.22105e6	−	9.04313e6i	0.558904	−	0.968050i
$615$	1.99409e6			0.212597
$616$	−59813.7			−0.00635110
$617$	−4.09890e6	+	7.09950e6i	−0.433465	+	0.750784i	−0.997169	−	0.0751933i	$-0.976043\pi$
$617$	−4.09890e6	+	7.09950e6i	−0.433465	+	0.750784i	0.563704	+	0.825977i	$0.309376\pi$
$618$	1.52337e6	−	2.63855e6i	0.160448	−	0.277903i
$619$	−7.12549e6			−0.747460			−0.373730	−	0.927537i	$-0.621921\pi$
$619$	−7.12549e6			−0.747460			−0.373730	+	0.927537i	$0.621921\pi$
$620$	−2.63573e6			−0.275373
$621$	1.72573e6	−	2.98905e6i	0.179574	−	0.311031i
$622$	2.59210e6	+	4.48965e6i	0.268643	+	0.465304i
$623$	507068.	−	878268.i	0.0523415	−	0.0906582i
$624$	305639.	+	529382.i	0.0314230	+	0.0544262i
$625$	−1.45177e6	−	2.51453e6i	−0.148661	−	0.257488i
$626$	70008.7			0.00714030
$627$	511059.	−	2.42543e6i	0.0519161	−	0.246389i
$628$	6.54963e6			0.662701
$629$	−308434.	−	534224.i	−0.0310839	−	0.0538389i
$630$	56127.9	+	97216.3i	0.00563414	+	0.00975861i
$631$	−5.45774e6	+	9.45308e6i	−0.545682	+	0.945148i	0.452882	+	0.891571i	$0.350396\pi$
$631$	−5.45774e6	+	9.45308e6i	−0.545682	+	0.945148i	−0.998564	+	0.0535780i	$0.982937\pi$
$632$	3.14225e6	+	5.44253e6i	0.312930	+	0.542011i
$633$	−1.11932e7	+	1.93872e7i	−1.11031	+	1.92311i
$634$	1.08603e7			1.07304
$635$	2.08597e6			0.205293
$636$	4.26726e6	−	7.39111e6i	0.418318	−	0.724548i
$637$	1.08956e6	−	1.88718e6i	0.106391	−	0.184274i
$638$	−1.12881e6			−0.109792
$639$	5.42567e6			0.525655
$640$	−231744.	+	401392.i	−0.0223644	+	0.0387363i
$641$	−6.97466e6	−	1.20805e7i	−0.670468	−	1.16128i	−0.977772	−	0.209673i	$-0.932760\pi$
$641$	−6.97466e6	−	1.20805e7i	−0.670468	−	1.16128i	0.307304	−	0.951611i	$-0.400573\pi$
$642$	−3.86810e6	+	6.69974e6i	−0.370391	+	0.641535i
$643$	4.93586e6	+	8.54916e6i	0.470799	+	0.815447i	0.999442	−	0.0333966i	$-0.0106324\pi$
$643$	4.93586e6	+	8.54916e6i	0.470799	+	0.815447i	−0.528643	+	0.848844i	$0.677299\pi$
$644$	−108085.	−	187209.i	−0.0102695	−	0.0177873i
$645$	−469287.			−0.0444160
$646$	−2.87203e6	+	938801.i	−0.270775	+	0.0885100i
$647$	−1.36427e7			−1.28127			−0.640633	−	0.767847i	$-0.721328\pi$
$647$	−1.36427e7			−1.28127			−0.640633	+	0.767847i	$0.721328\pi$
$648$	−2.33303e6	−	4.04092e6i	−0.218264	−	0.378045i
$649$	409574.	+	709402.i	0.0381698	+	0.0661121i
$650$	−607083.	+	1.05150e6i	−0.0563591	+	0.0976169i
$651$	−577725.	−	1.00065e6i	−0.0534280	−	0.0925400i
$652$	−3.64383e6	+	6.31130e6i	−0.335691	+	0.581434i
$653$	1.61238e7			1.47974			0.739870	−	0.672750i	$-0.234887\pi$
$653$	1.61238e7			1.47974			0.739870	+	0.672750i	$0.234887\pi$
$654$	1.55549e7			1.42208
$655$	−4.53674e6	+	7.85786e6i	−0.413181	+	0.715650i
$656$	−493382.	+	854563.i	−0.0447635	+	0.0775327i
$657$	3.28002e6			0.296458
$658$	465490.			0.0419127
$659$	−5.14764e6	+	8.91597e6i	−0.461737	+	0.799751i	−0.999048	−	0.0436328i	$-0.986107\pi$
$659$	−5.14764e6	+	8.91597e6i	−0.461737	+	0.799751i	0.537311	+	0.843384i	$0.319440\pi$
$660$	356489.	+	617457.i	0.0318557	+	0.0551756i
$661$	−7.67564e6	+	1.32946e7i	−0.683299	+	1.18351i	0.290669	+	0.956824i	$0.406122\pi$
$661$	−7.67564e6	+	1.32946e7i	−0.683299	+	1.18351i	−0.973968	+	0.226685i	$0.927211\pi$
$662$	2.62448e6	+	4.54573e6i	0.232755	+	0.403143i
$663$	−573137.	−	992702.i	−0.0506377	−	0.0877071i
$664$	−2.93180e6			−0.258056
$665$	99583.2	−	472612.i	0.00873236	−	0.0414429i
$666$	469957.			0.0410556
$667$	−2.03980e6	−	3.53303e6i	−0.177530	−	0.307492i
$668$	−1.86546e6	−	3.23107e6i	−0.161750	−	0.280160i
$669$	88145.0	−	152672.i	0.00761434	−	0.0131884i
$670$	3.93212e6	+	6.81063e6i	0.338407	+	0.586139i
$671$	−59463.3	+	102993.i	−0.00509850	+	0.00883087i
$672$	−203184.			−0.0173566
$673$	−2.04232e6			−0.173814			−0.0869071	−	0.996216i	$-0.527698\pi$
$673$	−2.04232e6			−0.173814			−0.0869071	+	0.996216i	$0.527698\pi$
$674$	−3.34126e6	+	5.78724e6i	−0.283309	+	0.490706i
$675$	3.22185e6	−	5.58041e6i	0.272174	−	0.471419i
$676$	−5.66791e6			−0.477042
$677$	−4.89781e6			−0.410706			−0.205353	−	0.978688i	$-0.565834\pi$
$677$	−4.89781e6			−0.410706			−0.205353	+	0.978688i	$0.565834\pi$
$678$	217076.	−	375987.i	0.0181359	−	0.0314122i
$679$	−148147.	−	256598.i	−0.0123316	−	0.0213589i
$680$	434568.	−	752694.i	0.0360400	−	0.0624232i
$681$	−1.01255e7	−	1.75378e7i	−0.836658	−	1.44913i
$682$	−1.00318e6	−	1.73755e6i	−0.0825879	−	0.143046i
$683$	−1.94967e7			−1.59922			−0.799612	−	0.600518i	$-0.794961\pi$
$683$	−1.94967e7			−1.59922			−0.799612	+	0.600518i	$0.794961\pi$
$684$	474622.	−	2.25251e6i	0.0387889	−	0.184088i
$685$	299987.			0.0244273
$686$	726879.	+	1.25899e6i	0.0589728	+	0.102144i
$687$	1.96664e6	+	3.40632e6i	0.158977	+	0.275356i
$688$	116112.	−	201112.i	0.00935204	−	0.0161982i
$689$	−1.90424e6	−	3.29823e6i	−0.152817	−	0.264687i
$690$	−1.28837e6	+	2.23153e6i	−0.103019	+	0.178435i
$691$	6.83906e6			0.544881			0.272440	−	0.962173i	$-0.412169\pi$
$691$	6.83906e6			0.544881			0.272440	+	0.962173i	$0.412169\pi$
$692$	−9.52436e6			−0.756085
$693$	−42725.3	+	74002.5i	−0.00337950	+	0.00585347i
$694$	−2.72798e6	+	4.72500e6i	−0.215002	+	0.372395i
$695$	4.70637e6			0.369593
$696$	−3.83452e6			−0.300046
$697$	925195.	−	1.60248e6i	0.0721359	−	0.124943i
$698$	997724.	+	1.72811e6i	0.0775125	+	0.134256i
$699$	−737827.	+	1.27795e6i	−0.0571165	+	0.0989286i
$700$	−201789.	−	349509.i	−0.0155651	−	0.0269596i
$701$	−7.30282e6	−	1.26489e7i	−0.561301	−	0.972201i	−0.997383	−	0.0722947i	$-0.976968\pi$
$701$	−7.30282e6	−	1.26489e7i	−0.561301	−	0.972201i	0.436083	−	0.899907i	$-0.356366\pi$
$702$	−1.44766e6			−0.110873
$703$	−1.50505e6	−	1.35034e6i	−0.114858	−	0.103052i
$704$	−352813.			−0.0268295
$705$	−2.77432e6	−	4.80526e6i	−0.210225	−	0.364120i
$706$	782679.	+	1.35564e6i	0.0590979	+	0.102361i
$707$	569965.	−	987209.i	0.0428845	−	0.0742781i
$708$	1.39130e6	+	2.40980e6i	0.104313	+	0.180675i
$709$	−2.09065e6	+	3.62112e6i	−0.156195	+	0.270537i	−0.933493	−	0.358594i	$-0.883256\pi$
$709$	−2.09065e6	+	3.62112e6i	−0.156195	+	0.270537i	0.777299	+	0.629132i	$0.216589\pi$
$710$	6.71485e6			0.499908
$711$	8.97812e6			0.666057
$712$	2.99096e6	−	5.18050e6i	0.221111	−	0.382976i
$713$	3.62553e6	−	6.27961e6i	0.267084	−	0.462603i
$714$	381012.			0.0279700
$715$	318162.			0.0232746
$716$	3.61697e6	−	6.26478e6i	0.263671	−	0.456692i
$717$	5.22105e6	+	9.04312e6i	0.379280	+	0.656932i
$718$	−1.22311e6	+	2.11849e6i	−0.0885430	+	0.153361i
$719$	2.84391e6	+	4.92579e6i	0.205160	+	0.355348i	0.950184	−	0.311690i	$-0.100895\pi$
$719$	2.84391e6	+	4.92579e6i	0.205160	+	0.355348i	−0.745024	+	0.667038i	$0.767562\pi$
$720$	331072.	+	573434.i	0.0238008	+	0.0412242i
$721$	451915.			0.0323756
$722$	−7.99218e6	+	5.84997e6i	−0.570587	+	0.417648i
$723$	2.49042e6			0.177185
$724$	−748227.	−	1.29597e6i	−0.0530502	−	0.0918856i
$725$	−3.80820e6	−	6.59600e6i	−0.269076	−	0.466054i
$726$	5.61906e6	−	9.73250e6i	0.395660	−	0.685304i
$727$	1.03655e7	+	1.79535e7i	0.727366	+	1.25983i	0.957993	+	0.286792i	$0.0925889\pi$
$727$	1.03655e7	+	1.79535e7i	0.727366	+	1.25983i	−0.230627	+	0.973042i	$0.574078\pi$
$728$	−45334.7	+	78522.0i	−0.00317031	+	0.00549114i
$729$	5.65151e6			0.393863
$730$	4.05938e6			0.281937
$731$	−217734.	+	377127.i	−0.0150707	+	0.0261032i
$732$	−201994.	+	349863.i	−0.0139335	+	0.0241335i
$733$	1.42537e7			0.979867			0.489934	−	0.871760i	$-0.337021\pi$
$733$	1.42537e7			0.979867			0.489934	+	0.871760i	$0.337021\pi$
$734$	1.03627e7			0.709960
$735$	4.31697e6	−	7.47721e6i	0.294755	−	0.510530i
$736$	−637543.	−	1.10426e6i	−0.0433826	−	0.0751408i
$737$	−2.99319e6	+	5.18435e6i	−0.202986	+	0.351581i
$738$	704853.	+	1.22084e6i	0.0476385	+	0.0825123i
$739$	−1.38098e6	−	2.39193e6i	−0.0930200	−	0.161115i	0.815761	−	0.578390i	$-0.196319\pi$
$739$	−1.38098e6	−	2.39193e6i	−0.0930200	−	0.161115i	−0.908781	+	0.417274i	$0.862985\pi$
$740$	581622.			0.0390447
$741$	−2.79670e6	−	2.50922e6i	−0.187112	−	0.167878i
$742$	1.26591e6			0.0844095
$743$	1.26290e7	+	2.18741e7i	0.839261	+	1.45364i	0.890514	+	0.454956i	$0.150345\pi$
$743$	1.26290e7	+	2.18741e7i	0.839261	+	1.45364i	−0.0512533	+	0.998686i	$0.516322\pi$
$744$	−3.40773e6	−	5.90237e6i	−0.225701	−	0.390925i
$745$	2.80462e6	−	4.85775e6i	0.185133	−	0.320660i
$746$	−6.80957e6	−	1.17945e7i	−0.447994	−	0.775949i
$747$	−2.09420e6	+	3.62727e6i	−0.137315	+	0.237836i
$748$	661598.			0.0432355
$749$	−1.14749e6			−0.0747386
$750$	−5.63867e6	+	9.76646e6i	−0.366036	+	0.633992i
$751$	7.08485e6	−	1.22713e7i	0.458385	−	0.793947i	−0.540490	−	0.841350i	$-0.681761\pi$
$751$	7.08485e6	−	1.22713e7i	0.458385	−	0.793947i	0.998876	+	0.0474034i	$0.0150946\pi$
$752$	2.74571e6			0.177056
$753$	334842.			0.0215205
$754$	−855564.	+	1.48188e6i	−0.0548055	+	0.0949259i
$755$	−2.13718e6	−	3.70170e6i	−0.136450	−	0.236338i
$756$	240596.	−	416725.i	0.0153103	−	0.0265182i
$757$	5.33854e6	+	9.24663e6i	0.338597	+	0.586467i	0.984169	−	0.177232i	$-0.0567143\pi$
$757$	5.33854e6	+	9.24663e6i	0.338597	+	0.586467i	−0.645572	+	0.763699i	$0.723381\pi$
$758$	−7.53052e6	−	1.30432e7i	−0.476049	−	0.824542i
$759$	−1.96145e6			−0.123587
$760$	587395.	−	2.78772e6i	0.0368890	−	0.175071i
$761$	−1.10719e7			−0.693041			−0.346520	−	0.938042i	$-0.612637\pi$
$761$	−1.10719e7			−0.693041			−0.346520	+	0.938042i	$0.612637\pi$
$762$	2.69695e6	+	4.67126e6i	0.168262	+	0.291438i
$763$	1.15361e6	+	1.99812e6i	0.0717379	+	0.124254i
$764$	1.08809e6	−	1.88462e6i	0.0674420	−	0.116813i
$765$	−620830.	−	1.07531e6i	−0.0383547	−	0.0664324i
$766$	4.23942e6	−	7.34289e6i	0.261056	−	0.452163i
$767$	1.24172e6			0.0762138
$768$	−1.19849e6			−0.0733213
$769$	3.57364e6	−	6.18973e6i	0.217919	−	0.377447i	−0.736253	−	0.676707i	$-0.763406\pi$
$769$	3.57364e6	−	6.18973e6i	0.217919	−	0.377447i	0.954172	+	0.299260i	$0.0967398\pi$
$770$	−52877.2	+	91586.0i	−0.00321397	+	0.00556676i
$771$	7.42051e6			0.449571
$772$	−5.88129e6			−0.355164
$773$	−2.13245e6	+	3.69351e6i	−0.128360	+	0.222326i	−0.923041	−	0.384701i	$-0.874305\pi$
$773$	−2.13245e6	+	3.69351e6i	−0.128360	+	0.222326i	0.794681	+	0.607027i	$0.207638\pi$
$774$	−165879.	−	287312.i	−0.00995268	−	0.0172385i
$775$	6.76869e6	−	1.17237e7i	0.404809	−	0.701150i
$776$	−873851.	−	1.51355e6i	−0.0520934	−	0.0902285i
$777$	127486.	+	220812.i	0.00757547	+	0.0131211i
$778$	−1.59627e7			−0.945488
$779$	1.25056e6	−	5.93505e6i	0.0738350	−	0.350414i
$780$	1.08078e6			0.0636063
$781$	2.55572e6	+	4.42664e6i	0.149929	+	0.259685i
$782$	1.19553e6	+	2.07071e6i	0.0699105	+	0.121089i
$783$	4.54057e6	−	7.86450e6i	0.264671	−	0.458423i
$784$	2.13623e6	+	3.70005e6i	0.124124	+	0.214990i
$785$	5.79008e6	−	1.00287e7i	0.335360	−	0.580860i
$786$	−2.34622e7			−1.35460
$787$	−1.69486e6			−0.0975430			−0.0487715	−	0.998810i	$-0.515531\pi$
$787$	−1.69486e6			−0.0975430			−0.0487715	+	0.998810i	$0.515531\pi$
$788$	6.10018e6	−	1.05658e7i	0.349967	−	0.606160i
$789$	−4.36331e6	+	7.55748e6i	−0.249531	+	0.432200i
$790$	1.11114e7			0.633433
$791$	64396.8			0.00365951
$792$	−252017.	+	436506.i	−0.0142763	+	0.0247274i
$793$	90138.3	+	156124.i	0.00509010	+	0.00881631i
$794$	3.99312e6	−	6.91629e6i	0.224782	−	0.389334i
$795$	−7.54479e6	−	1.30680e7i	−0.423379	−	0.733314i
$796$	3.27307e6	+	5.66912e6i	0.183093	+	0.317127i
$797$	2.57195e7			1.43422			0.717111	−	0.696959i	$-0.245464\pi$
$797$	2.57195e7			1.43422			0.717111	+	0.696959i	$0.245464\pi$
$798$	1.18710e6	−	388037.i	0.0659905	−	0.0215708i
$799$	−5.14878e6			−0.285324
$800$	−1.19026e6	−	2.06159e6i	−0.0657533	−	0.113888i
$801$	−4.27293e6	−	7.40094e6i	−0.235312	−	0.407573i
$802$	−6.09685e6	+	1.05601e7i	−0.334711	+	0.579736i
$803$	1.54503e6	+	2.67607e6i	0.0845565	+	0.146456i
$804$	−1.01677e7	+	1.76110e7i	−0.554731	+	0.960822i
$805$	−382202.			−0.0207876
$806$	−3.04136e6			−0.164903
$807$	1.84597e7	−	3.19731e7i	0.997792	−	1.72823i
$808$	3.36196e6	−	5.82309e6i	0.181161	−	0.313780i
$809$	−1.93803e7			−1.04109			−0.520546	−	0.853833i	$-0.674272\pi$
$809$	−1.93803e7			−1.04109			−0.520546	+	0.853833i	$0.674272\pi$
$810$	−8.24989e6			−0.441810
$811$	9.79939e6	−	1.69730e7i	0.523175	−	0.906166i	−0.476461	−	0.879196i	$-0.658081\pi$
$811$	9.79939e6	−	1.69730e7i	0.523175	−	0.906166i	0.999636	−	0.0269704i	$-0.00858598\pi$
$812$	−284383.	−	492565.i	−0.0151361	−	0.0262164i
$813$	−2.06433e7	+	3.57553e7i	−1.09535	+	1.89720i
$814$	221370.	+	383423.i	0.0117100	+	0.0202823i
$815$	6.44253e6	+	1.11588e7i	0.339752	+	0.588468i
$816$	2.24741e6			0.118156
$817$	−294306.	+	1.39675e6i	−0.0154257	+	0.0732088i
$818$	−2.06504e7			−1.07906
$819$	64765.8	+	112178.i	0.00337393	+	0.00584382i
$820$	872332.	+	1.51092e6i	0.0453051	+	0.0784707i
$821$	−1.15624e6	+	2.00266e6i	−0.0598671	+	0.103693i	−0.894406	−	0.447257i	$-0.852401\pi$
$821$	−1.15624e6	+	2.00266e6i	−0.0598671	+	0.103693i	0.834539	+	0.550950i	$0.185734\pi$
$822$	387853.	+	671782.i	0.0200211	+	0.0346776i
$823$	1.31184e7	−	2.27217e7i	0.675120	−	1.16934i	−0.301314	−	0.953525i	$-0.597425\pi$
$823$	1.31184e7	−	2.27217e7i	0.675120	−	1.16934i	0.976434	−	0.215817i	$-0.0692414\pi$
$824$	2.66564e6			0.136767
$825$	−3.66194e6			−0.187317
$826$	−206368.	+	357440.i	−0.0105243	+	0.0182286i
$827$	−1.30567e7	+	2.26149e7i	−0.663850	+	1.14982i	0.315745	+	0.948844i	$0.397746\pi$
$827$	−1.30567e7	+	2.26149e7i	−0.663850	+	1.14982i	−0.979596	+	0.200979i	$0.935588\pi$
$828$	−1.82161e6			−0.0923377
$829$	−1.68937e7			−0.853765			−0.426883	−	0.904307i	$-0.640388\pi$
$829$	−1.68937e7			−0.853765			−0.426883	+	0.904307i	$0.640388\pi$
$830$	−2.59180e6	+	4.48914e6i	−0.130589	+	0.226187i
$831$	1.91821e6	+	3.32244e6i	0.0963593	+	0.166899i
$832$	−267408.	+	463165.i	−0.0133927	+	0.0231968i
$833$	−4.00587e6	−	6.93837e6i	−0.200025	−	0.346454i
$834$	6.08487e6	+	1.05393e7i	0.302926	+	0.524683i
$835$	−6.59651e6			−0.327414
$836$	2.06132e6	−	673797.i	0.102007	−	0.0333437i
$837$	1.61408e7			0.796364
$838$	4.21252e6	+	7.29629e6i	0.207220	+	0.358915i
$839$	1.09468e7	+	1.89604e7i	0.536887	+	0.929915i	0.999069	+	0.0431304i	$0.0137331\pi$
$839$	1.09468e7	+	1.89604e7i	0.536887	+	0.929915i	−0.462183	+	0.886785i	$0.652934\pi$
$840$	−179621.	+	311113.i	−0.00878332	+	0.0152132i
$841$	4.88866e6	+	8.46740e6i	0.238341	+	0.412819i
$842$	4.42426e6	−	7.66304e6i	0.215060	−	0.372495i
$843$	−4.15683e7			−2.01462
$844$	−1.95862e7			−0.946442
$845$	−5.01061e6	+	8.67864e6i	−0.241407	+	0.418129i
$846$	1.96128e6	−	3.39704e6i	0.0942138	−	0.163183i
$847$	1.66692e6			0.0798376
$848$	7.46699e6			0.356579
$849$	−5.07958e6	+	8.79809e6i	−0.241857	+	0.418909i
$850$	2.23199e6	+	3.86592e6i	0.105961	+	0.183529i
$851$	−800042.	+	1.38571e6i	−0.0378694	+	0.0655918i
$852$	8.68164e6	+	1.50370e7i	0.409735	+	0.709681i
$853$	1.50621e7	+	2.60883e7i	0.708781	+	1.22765i	0.965309	+	0.261108i	$0.0840880\pi$
$853$	1.50621e7	+	2.60883e7i	0.708781	+	1.22765i	−0.256528	+	0.966537i	$0.582579\pi$
$854$	−59922.5			−0.00281154
$855$	−3.02943e6	−	2.71802e6i	−0.141725	−	0.127156i
$856$	−6.76852e6			−0.315725
$857$	1.33849e7	+	2.31833e7i	0.622535	+	1.07826i	0.989012	+	0.147835i	$0.0472303\pi$
$857$	1.33849e7	+	2.31833e7i	0.622535	+	1.07826i	−0.366478	+	0.930427i	$0.619436\pi$
$858$	411352.	+	712482.i	0.0190763	+	0.0330412i
$859$	−5.03346e6	+	8.71821e6i	−0.232747	+	0.403129i	−0.958615	−	0.284704i	$-0.908105\pi$
$859$	−5.03346e6	+	8.71821e6i	−0.232747	+	0.403129i	0.725869	+	0.687833i	$0.241438\pi$
$860$	−205294.	−	355579.i	−0.00946519	−	0.0163942i
$861$	−382413.	+	662359.i	−0.0175802	+	0.0304499i
$862$	−9.49881e6			−0.435413
$863$	−1.92879e7			−0.881574			−0.440787	−	0.897612i	$-0.645301\pi$
$863$	−1.92879e7			−0.881574			−0.440787	+	0.897612i	$0.645301\pi$
$864$	1.41916e6	−	2.45807e6i	0.0646768	−	0.112024i
$865$	−8.41984e6	+	1.45836e7i	−0.382616	+	0.662711i
$866$	2.20904e7			1.00094
$867$	2.17512e7			0.982734
$868$	505461.	−	875484.i	0.0227713	−	0.0394411i
$869$	4.22907e6	+	7.32497e6i	0.189975	+	0.329046i
$870$	−3.38984e6	+	5.87137e6i	−0.151838	+	0.262991i
$871$	4.53726e6	+	7.85877e6i	0.202651	+	0.351002i
$872$	6.80463e6	+	1.17860e7i	0.303049	+	0.524897i
$873$	−2.49679e6			−0.110878
$874$	5.83375e6	+	5.23407e6i	0.258327	+	0.231772i
$875$	−1.67274e6			−0.0738599
$876$	5.24837e6	+	9.09045e6i	0.231081	+	0.400244i
$877$	4.40995e6	+	7.63826e6i	0.193613	+	0.335348i	0.946445	−	0.322865i	$-0.104646\pi$
$877$	4.40995e6	+	7.63826e6i	0.193613	+	0.335348i	−0.752832	+	0.658213i	$0.771313\pi$
$878$	1.26733e7	−	2.19507e7i	0.554820	−	0.960977i
$879$	−9.46301e6	−	1.63904e7i	−0.413102	−	0.715513i
$880$	−311898.	+	540224.i	−0.0135771	+	0.0235162i
$881$	−3.50587e7			−1.52179			−0.760897	−	0.648872i	$-0.775241\pi$
$881$	−3.50587e7			−1.52179			−0.760897	+	0.648872i	$0.775241\pi$
$882$	6.10369e6			0.264193
$883$	1.76431e7	−	3.05587e7i	0.761505	−	1.31896i	−0.180570	−	0.983562i	$-0.557794\pi$
$883$	1.76431e7	−	3.05587e7i	0.761505	−	1.31896i	0.942075	−	0.335403i	$-0.108872\pi$
$884$	501447.	−	868531.i	0.0215821	−	0.0373813i
$885$	4.91981e6			0.211150
$886$	1.61550e7			0.691388
$887$	3.08735e6	−	5.34745e6i	0.131758	−	0.228212i	−0.792596	−	0.609747i	$-0.791271\pi$
$887$	3.08735e6	−	5.34745e6i	0.131758	−	0.228212i	0.924354	+	0.381535i	$0.124604\pi$
$888$	751980.	+	1.30247e6i	0.0320018	+	0.0554287i
$889$	−400032.	+	692877.i	−0.0169762	+	0.0294037i
$890$	−5.28821e6	−	9.15945e6i	−0.223787	−	0.387610i
$891$	−3.13997e6	−	5.43858e6i	−0.132505	−	0.229505i
$892$	154239.			0.00649056
$893$	−1.60419e7	+	5.24372e6i	−0.673173	+	0.220044i
$894$	1.45044e7			0.606954
$895$	−6.39504e6	−	1.10765e7i	−0.266861	−	0.462218i
$896$	−88884.4	−	153952.i	−0.00369875	−	0.00640643i
$897$	−1.48665e6	+	2.57495e6i	−0.0616918	+	0.106853i
$898$	−1.30394e7	−	2.25850e7i	−0.539595	−	0.934607i
$899$	9.53915e6	−	1.65223e7i	0.393650	−	0.681822i
$900$	−3.40085e6			−0.139953
$901$	−1.40022e7			−0.574623
$902$	−664031.	+	1.15014e6i	−0.0271752	+	0.0470688i
$903$	89996.7	−	155879.i	0.00367288	−	0.00636162i
$904$	379847.			0.0154592
$905$	−2.64583e6			−0.107384
$906$	5.52632e6	−	9.57186e6i	0.223674	−	0.387414i
$907$	−1.80758e7	−	3.13082e7i	−0.729590	−	1.26369i	−0.957057	−	0.289901i	$-0.906378\pi$
$907$	−1.80758e7	−	3.13082e7i	−0.729590	−	1.26369i	0.227467	−	0.973786i	$-0.426956\pi$
$908$	8.85895e6	−	1.53441e7i	0.356589	−	0.617630i
$909$	−4.80295e6	−	8.31895e6i	−0.192796	−	0.333933i
$910$	80154.6	+	138832.i	0.00320867	+	0.00555758i
$911$	9.93057e6			0.396441			0.198220	−	0.980157i	$-0.436484\pi$
$911$	9.93057e6			0.396441			0.198220	+	0.980157i	$0.436484\pi$
$912$	7.00218e6	−	2.28885e6i	0.278770	−	0.0911235i
$913$	−3.94584e6			−0.156661
$914$	7.79206e6	+	1.34962e7i	0.308522	+	0.534376i
$915$	357138.	+	618581.i	0.0141021	+	0.0244255i
$916$	−1.72065e6	+	2.98025e6i	−0.0677568	+	0.117358i
$917$	−1.74005e6	−	3.01385e6i	−0.0683341	−	0.118358i
$918$	−2.66123e6	+	4.60939e6i	−0.104226	+	0.180525i
$919$	−3.12833e7			−1.22187			−0.610933	−	0.791682i	$-0.709206\pi$
$919$	−3.12833e7			−1.22187			−0.610933	+	0.791682i	$0.709206\pi$
$920$	−2.25444e6			−0.0878149
$921$	2.38700e7	−	4.13440e7i	0.927262	−	1.60606i
$922$	1.57287e7	−	2.72429e7i	0.609349	−	1.05542i
$923$	7.74824e6			0.299364
$924$	−273460.			−0.0105369
$925$	−1.49364e6	+	2.58706e6i	−0.0573973	+	0.0994150i
$926$	−9.08448e6	−	1.57348e7i	−0.348155	−	0.603022i
$927$	1.90408e6	−	3.29797e6i	0.0727758	−	0.126051i
$928$	−1.67744e6	−	2.90541e6i	−0.0639407	−	0.110749i
$929$	−1.93607e6	−	3.35337e6i	−0.0736007	−	0.127480i	0.826876	−	0.562384i	$-0.190116\pi$
$929$	−1.93607e6	−	3.35337e6i	−0.0736007	−	0.127480i	−0.900477	+	0.434904i	$0.856782\pi$
$930$	−1.20502e7			−0.456863
$931$	−1.95472e7	−	1.75379e7i	−0.739114	−	0.663137i
$932$	−1.29107e6			−0.0486868
$933$	1.18507e7	+	2.05261e7i	0.445699	+	0.771973i
$934$	4.16493e6	+	7.21387e6i	0.156221	+	0.270583i
$935$	584874.	−	1.01303e6i	0.0218793	−	0.0378961i
$936$	382024.	+	661684.i	0.0142528	+	0.0246866i
$937$	2.36314e7	−	4.09307e7i	0.879306	−	1.52300i	0.0272014	−	0.999630i	$-0.491340\pi$
$937$	2.36314e7	−	4.09307e7i	0.879306	−	1.52300i	0.852104	−	0.523372i	$-0.175326\pi$
$938$	−3.01630e6			−0.111935
$939$	320070.			0.0118463
$940$	2.42730e6	−	4.20420e6i	0.0895991	−	0.155190i
$941$	−1.49237e7	+	2.58486e7i	−0.549418	+	0.951620i	0.448896	+	0.893584i	$0.351817\pi$
$941$	−1.49237e7	+	2.58486e7i	−0.549418	+	0.951620i	−0.998314	+	0.0580362i	$0.981516\pi$
$942$	2.99440e7			1.09947
$943$	−4.79969e6			−0.175766
$944$	−1.21727e6	+	2.10837e6i	−0.0444587	+	0.0770048i
$945$	−425389.	−	736796.i	−0.0154955	−	0.0268391i
$946$	156272.	−	270672.i	0.00567746	−	0.00983366i
$947$	1.69981e7	+	2.94416e7i	0.615922	+	1.06681i	0.990222	+	0.139501i	$0.0445498\pi$
$947$	1.69981e7	+	2.94416e7i	0.615922	+	1.06681i	−0.374300	+	0.927308i	$0.622117\pi$
$948$	1.43659e7	+	2.48825e7i	0.519174	+	0.899235i
$949$	4.68410e6			0.168834
$950$	1.08913e7	+	9.77176e6i	0.391536	+	0.351288i
$951$	4.96517e7			1.78026
$952$	166677.	+	288693.i	0.00596050	+	0.0103239i
$953$	−1.68409e7	−	2.91693e7i	−0.600666	−	1.04038i	−0.992720	−	0.120441i	$-0.961569\pi$
$953$	−1.68409e7	−	2.91693e7i	−0.600666	−	1.04038i	0.392055	−	0.919942i	$-0.371764\pi$
$954$	5.33373e6	−	9.23829e6i	0.189740	−	0.328640i
$955$	−1.92381e6	−	3.33214e6i	−0.0682580	−	0.118226i
$956$	−4.56798e6	+	7.91197e6i	−0.161651	+	0.279988i
$957$	−5.16079e6			−0.182153
$958$	−2.59723e7			−0.914317
$959$	−57529.4	+	99643.8i	−0.00201996	+	0.00349868i
$960$	−1.05950e6	+	1.83511e6i	−0.0371042	+	0.0642664i
$961$	5.28058e6			0.184448
$962$	671132.			0.0233814
$963$	−4.83481e6	+	8.37413e6i	−0.168002	+	0.290987i
$964$	1.08945e6	+	1.88699e6i	0.0377586	+	0.0653999i
$965$	−5.19925e6	+	9.00537e6i	−0.179731	+	0.311303i
$966$	−494150.	−	855893.i	−0.0170379	−	0.0295105i
$967$	1.06177e6	+	1.83903e6i	0.0365143	+	0.0632446i	0.883705	−	0.468044i	$-0.155041\pi$
$967$	1.06177e6	+	1.83903e6i	0.0365143	+	0.0632446i	−0.847191	+	0.531289i	$0.821708\pi$
$968$	9.83242e6			0.337266
$969$	−1.31306e7	+	4.29207e6i	−0.449235	+	0.146844i
$970$	−3.09005e6			−0.105447
$971$	2.28632e7	+	3.96002e7i	0.778195	+	1.34787i	0.932981	+	0.359925i	$0.117198\pi$
$971$	2.28632e7	+	3.96002e7i	0.778195	+	1.34787i	−0.154787	+	0.987948i	$0.549469\pi$
$972$	−5.27790e6	−	9.14159e6i	−0.179182	−	0.310353i
$973$	−902554.	+	1.56327e6i	−0.0305627	+	0.0529361i
$974$	−5.01796e6	−	8.69137e6i	−0.169485	−	0.293556i
$975$	−2.77550e6	+	4.80731e6i	−0.0935039	+	0.161954i
$976$	−353455.			−0.0118771
$977$	2.43356e7			0.815652			0.407826	−	0.913060i	$-0.366287\pi$
$977$	2.43356e7			0.815652			0.407826	+	0.913060i	$0.366287\pi$
$978$	−1.66591e7	+	2.88544e7i	−0.556935	+	0.964640i
$979$	4.02546e6	−	6.97231e6i	0.134233	−	0.232498i
$980$	7.55397e6			0.251252
$981$	1.94424e7			0.645026
$982$	−1.50332e7	+	2.60383e7i	−0.497478	+	0.861657i
$983$	−6.85561e6	−	1.18743e7i	−0.226288	−	0.391943i	0.730417	−	0.683002i	$-0.239326\pi$
$983$	−6.85561e6	−	1.18743e7i	−0.226288	−	0.391943i	−0.956705	+	0.291059i	$0.905993\pi$
$984$	−2.25568e6	+	3.90695e6i	−0.0742659	+	0.128632i
$985$	−1.07855e7	−	1.86810e7i	−0.354201	−	0.613494i
$986$	3.14555e6	+	5.44826e6i	0.103040	+	0.178470i
$987$	2.12816e6			0.0695363
$988$	677794.	−	3.21674e6i	0.0220905	−	0.104839i
$989$	1.12955e6			0.0367212
$990$	445582.	+	771771.i	0.0144491	+	0.0250265i
$991$	8.71071e6	+	1.50874e7i	0.281754	+	0.488011i	0.971817	−	0.235738i	$-0.0757506\pi$
$991$	8.71071e6	+	1.50874e7i	0.281754	+	0.488011i	−0.690063	+	0.723749i	$0.742417\pi$
$992$	2.98148e6	−	5.16408e6i	0.0961951	−	0.166615i
$993$	1.19988e7	+	2.07825e7i	0.386157	+	0.668843i
$994$	−1.28773e6	+	2.23041e6i	−0.0413388	+	0.0716009i
$995$	1.15740e7			0.370617
$996$	−1.34038e7			−0.428133
$997$	4.45133e6	−	7.70993e6i	0.141825	−	0.245647i	−0.786359	−	0.617770i	$-0.788036\pi$
$997$	4.45133e6	−	7.70993e6i	0.141825	−	0.245647i	0.928184	+	0.372122i	$0.121370\pi$
$998$	−1.24722e6	+	2.16025e6i	−0.0396385	+	0.0686559i
$999$	−3.56177e6			−0.112915

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.6.c.a.7.3	✓	6
3.2	odd	2		342.6.g.a.235.2		6
4.3	odd	2		304.6.i.a.273.1		6
19.7	even	3		722.6.a.e.1.1		3
19.11	even	3	inner	38.6.c.a.11.3	yes	6
19.12	odd	6		722.6.a.f.1.3		3
57.11	odd	6		342.6.g.a.163.2		6
76.11	odd	6		304.6.i.a.49.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.c.a.7.3	✓	6	1.1	even	1	trivial
38.6.c.a.11.3	yes	6	19.11	even	3	inner
304.6.i.a.49.1		6	76.11	odd	6
304.6.i.a.273.1		6	4.3	odd	2
342.6.g.a.163.2		6	57.11	odd	6
342.6.g.a.235.2		6	3.2	odd	2
722.6.a.e.1.1		3	19.7	even	3
722.6.a.f.1.3		3	19.12	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	38.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 3.46410i) q^{2} +(9.14373 + 15.8374i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(14.1445 + 24.4990i) q^{5} +(-36.5749 + 63.3496i) q^{6} -10.8501 q^{7} -64.0000 q^{8} +(-45.7157 + 79.1819i) q^{9} +O(q^{10})\)	\(q+(2.00000 + 3.46410i) q^{2} +(9.14373 + 15.8374i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(14.1445 + 24.4990i) q^{5} +(-36.5749 + 63.3496i) q^{6} -10.8501 q^{7} -64.0000 q^{8} +(-45.7157 + 79.1819i) q^{9} +(-56.5781 + 97.9961i) q^{10} -86.1360 q^{11} -292.599 q^{12} +(-65.2853 + 113.077i) q^{13} +(-21.7003 - 37.5860i) q^{14} +(-258.667 + 448.025i) q^{15} +(-128.000 - 221.703i) q^{16} +(240.027 + 415.738i) q^{17} -365.725 q^{18} +(1171.25 + 1050.85i) q^{19} -452.624 q^{20} +(-99.2108 - 171.838i) q^{21} +(-172.272 - 298.384i) q^{22} +(622.601 - 1078.38i) q^{23} +(-585.199 - 1013.59i) q^{24} +(1162.37 - 2013.28i) q^{25} -522.282 q^{26} +2771.81 q^{27} +(86.8012 - 150.344i) q^{28} +(1638.13 - 2837.32i) q^{29} -2069.34 q^{30} +5823.21 q^{31} +(512.000 - 886.810i) q^{32} +(-787.605 - 1364.17i) q^{33} +(-960.107 + 1662.95i) q^{34} +(-153.470 - 265.818i) q^{35} +(-731.451 - 1266.91i) q^{36} -1285.00 q^{37} +(-1297.75 + 6159.01i) q^{38} -2387.80 q^{39} +(-905.249 - 1567.94i) q^{40} +(-1927.28 - 3338.14i) q^{41} +(396.843 - 687.353i) q^{42} +(453.563 + 785.594i) q^{43} +(689.088 - 1193.54i) q^{44} -2586.50 q^{45} +4980.81 q^{46} +(-5362.72 + 9288.50i) q^{47} +(2340.80 - 4054.38i) q^{48} -16689.3 q^{49} +9298.92 q^{50} +(-4389.48 + 7602.80i) q^{51} +(-1044.56 - 1809.24i) q^{52} +(-14584.0 + 25260.2i) q^{53} +(5543.61 + 9601.82i) q^{54} +(-1218.35 - 2110.25i) q^{55} +694.409 q^{56} +(-5933.16 + 28158.2i) q^{57} +13105.0 q^{58} +(-4754.96 - 8235.84i) q^{59} +(-4138.68 - 7168.40i) q^{60} +(690.342 - 1195.71i) q^{61} +(11646.4 + 20172.2i) q^{62} +(496.022 - 859.135i) q^{63} +4096.00 q^{64} -3693.71 q^{65} +(3150.42 - 5456.69i) q^{66} +(34749.5 - 60188.0i) q^{67} -7680.85 q^{68} +22771.6 q^{69} +(613.880 - 1063.27i) q^{70} +(-29670.7 - 51391.2i) q^{71} +(2925.80 - 5067.64i) q^{72} +(-17937.1 - 31067.9i) q^{73} +(-2570.00 - 4451.37i) q^{74} +42513.4 q^{75} +(-23930.9 + 7822.47i) q^{76} +934.589 q^{77} +(-4775.61 - 8271.59i) q^{78} +(-49097.6 - 85039.5i) q^{79} +(3621.00 - 6271.75i) q^{80} +(36453.6 + 63139.4i) q^{81} +(7709.10 - 13352.6i) q^{82} +45809.3 q^{83} +3174.75 q^{84} +(-6790.12 + 11760.8i) q^{85} +(-1814.25 + 3142.37i) q^{86} +59914.4 q^{87} +5512.71 q^{88} +(-46733.8 + 80945.3i) q^{89} +(-5173.01 - 8959.91i) q^{90} +(708.354 - 1226.91i) q^{91} +(9961.61 + 17254.0i) q^{92} +(53245.8 + 92224.5i) q^{93} -42901.8 q^{94} +(-9178.05 + 43558.1i) q^{95} +18726.4 q^{96} +(13653.9 + 23649.3i) q^{97} +(-33378.5 - 57813.3i) q^{98} +(3937.77 - 6820.41i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12 q^{2} - 15 q^{3} - 48 q^{4} + 14 q^{5} + 60 q^{6} - 624 q^{7} - 384 q^{8} - 410 q^{9}+O(q^{10}) \) 6 * q + 12 * q^2 - 15 * q^3 - 48 * q^4 + 14 * q^5 + 60 * q^6 - 624 * q^7 - 384 * q^8 - 410 * q^9	\( 6 q + 12 q^{2} - 15 q^{3} - 48 q^{4} + 14 q^{5} + 60 q^{6} - 624 q^{7} - 384 q^{8} - 410 q^{9} - 56 q^{10} - 938 q^{11} + 480 q^{12} - 736 q^{13} - 1248 q^{14} + 954 q^{15} - 768 q^{16} - 1000 q^{17} - 3280 q^{18} + 5681 q^{19} - 448 q^{20} + 5816 q^{21} - 1876 q^{22} - 2168 q^{23} + 960 q^{24} - 3187 q^{25} - 5888 q^{26} + 16650 q^{27} + 4992 q^{28} + 1486 q^{29} + 7632 q^{30} + 396 q^{31} + 3072 q^{32} + 3589 q^{33} + 4000 q^{34} - 4992 q^{35} - 6560 q^{36} + 20060 q^{37} + 13528 q^{38} + 37480 q^{39} - 896 q^{40} - 19551 q^{41} - 23264 q^{42} - 5058 q^{43} + 7504 q^{44} - 114408 q^{45} - 17344 q^{46} + 7426 q^{47} - 3840 q^{48} - 1898 q^{49} - 25496 q^{50} - 51980 q^{51} - 11776 q^{52} - 3156 q^{53} + 33300 q^{54} + 8540 q^{55} + 39936 q^{56} - 60762 q^{57} + 11888 q^{58} - 325 q^{59} + 15264 q^{60} + 19674 q^{61} + 792 q^{62} + 82320 q^{63} + 24576 q^{64} - 149516 q^{65} - 14356 q^{66} + 61837 q^{67} + 32000 q^{68} + 64072 q^{69} + 19968 q^{70} + 5760 q^{71} + 26240 q^{72} + 18747 q^{73} + 40120 q^{74} + 219654 q^{75} - 36784 q^{76} + 107504 q^{77} + 74960 q^{78} + 80158 q^{79} + 3584 q^{80} - 59939 q^{81} + 78204 q^{82} - 335402 q^{83} - 186112 q^{84} + 102510 q^{85} + 20232 q^{86} + 125388 q^{87} + 60032 q^{88} - 166228 q^{89} - 228816 q^{90} + 136784 q^{91} - 34688 q^{92} + 368074 q^{93} + 59408 q^{94} - 171266 q^{95} - 30720 q^{96} - 86615 q^{97} - 3796 q^{98} + 28646 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 - 15 * q^3 - 48 * q^4 + 14 * q^5 + 60 * q^6 - 624 * q^7 - 384 * q^8 - 410 * q^9 - 56 * q^10 - 938 * q^11 + 480 * q^12 - 736 * q^13 - 1248 * q^14 + 954 * q^15 - 768 * q^16 - 1000 * q^17 - 3280 * q^18 + 5681 * q^19 - 448 * q^20 + 5816 * q^21 - 1876 * q^22 - 2168 * q^23 + 960 * q^24 - 3187 * q^25 - 5888 * q^26 + 16650 * q^27 + 4992 * q^28 + 1486 * q^29 + 7632 * q^30 + 396 * q^31 + 3072 * q^32 + 3589 * q^33 + 4000 * q^34 - 4992 * q^35 - 6560 * q^36 + 20060 * q^37 + 13528 * q^38 + 37480 * q^39 - 896 * q^40 - 19551 * q^41 - 23264 * q^42 - 5058 * q^43 + 7504 * q^44 - 114408 * q^45 - 17344 * q^46 + 7426 * q^47 - 3840 * q^48 - 1898 * q^49 - 25496 * q^50 - 51980 * q^51 - 11776 * q^52 - 3156 * q^53 + 33300 * q^54 + 8540 * q^55 + 39936 * q^56 - 60762 * q^57 + 11888 * q^58 - 325 * q^59 + 15264 * q^60 + 19674 * q^61 + 792 * q^62 + 82320 * q^63 + 24576 * q^64 - 149516 * q^65 - 14356 * q^66 + 61837 * q^67 + 32000 * q^68 + 64072 * q^69 + 19968 * q^70 + 5760 * q^71 + 26240 * q^72 + 18747 * q^73 + 40120 * q^74 + 219654 * q^75 - 36784 * q^76 + 107504 * q^77 + 74960 * q^78 + 80158 * q^79 + 3584 * q^80 - 59939 * q^81 + 78204 * q^82 - 335402 * q^83 - 186112 * q^84 + 102510 * q^85 + 20232 * q^86 + 125388 * q^87 + 60032 * q^88 - 166228 * q^89 - 228816 * q^90 + 136784 * q^91 - 34688 * q^92 + 368074 * q^93 + 59408 * q^94 - 171266 * q^95 - 30720 * q^96 - 86615 * q^97 - 3796 * q^98 + 28646 * q^99

Introduction

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